Question 33. a = ∠1 + ∠2 = 60° + 30° = 90°. Two lines in a plane which do not meet at a point anywhere are called _________ lines. In the given figure, examine whether the following pairs of lines are parallel or not: (a) Let an angle be x. 20-30 17 ⇒ ∠2 = 70° ——— (ii) (d) Let the angle be x. (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. always. Solution: Explain your answer. (d) 75° (a) 60°, 120° ⇒ 2∠ABP = 180° – 46° = 134 Then, Sign in:P. 1 decade ago. a: If two lines intersect, then the vertically opposite angles are equal. (b) 4th player has the greatest kicking angle. In the given figure, PA || BC || DT and AB || DC. Question 103. Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. In the given figure, QP || RS. (a) alternate exterior angles …, ar is her work place from herhouse?bor house. false . In the given figure, line l intersects two parallel lines PQ and RS. (b) corresponding angles From (i), Thus the required angles are 90° each. (iii) d and f Find the angles. (c) Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other. (c) 80 As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. Question 34. Being congruent means that these two angles would be equal to each other and hence they would be optically superimposable. Two supplementary angles always form a linear pair. If one of them is one-third of the other, find the angles. Its complementary angle must be less than 45°. ⇒ 4x + 4 = 180° ⇒ 4x = 180°- 4 = 176° ∴ ∠1 = 30° ——– (i) [Corresponding angles] Since, vertically opposite angles are equal. What is the type of other angle of a linear pair if Also, m || n and QR is a transversal. (iii) Two right angles cannot be complement of each other. is this your homework? ⇒ ∠z = 180° – 120° = 60° (a) 20° Question 7. (b) Now the players are lined up as shown in Fig. ⇒ 60° + 20 = 180° (c) both are acute Solution: \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) Solution: ∠2 = ∠4 [Corresponding angles] (c) complementary Now, p || q and n is a transversal. ∴ ∠POQ + ∠QOR = 180° [Linear pair] In the given figure, lines PQ and ST intersect at O. ∴ b = 70° [Corresponding angles] ⇒ 5b – 180° – 80° = 100° ⇒ y = 180° – 48° = 132° Solution: Find the values of a, b and c. These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. Then, ∠QOS measures ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] We know that when the measure of an angle is exactly 90°, then it is known as a right angle. Solution: Solution: Also, BC || DT and DC is a transversal. ∴ ∠PQT = ∠LTQ [Alternate interior angles] In the given figure, PO || RS. (c) (45°, 45°) and (60°, 30°) are the two pairs of angles formed by different positions of two players such that they are complement to each other. In the given figure, two parallel lines l and m are cut by two transversals p and 4. In the given figure, a and bare (c) p is false and q is true \(\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}\) (d) both are obtuse ⇒ x = 360°- 210° \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) (c) 85° (a) Since, POQ is a straight line. Solution: Answer. The angles x – 10° and 190° – x are Two angles are making a linear pair. According to question, (e) Since, POQ is a straight line. If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is Two angles forming a _________ pair are supplementary. (b) 100° Solution: (i) EF and GH Also, p || q and l is a transversal. ∴ ∠RSC + ∠CSF = 180° [Linear pair] ∠6 = ∠7 [Alternate exterior angles] Again, ∠PQR and ∠QRP are complementary as ∠PQR + ∠QRP = 40° + 50° = 90°. My answer-- Vertical angles If not, then one is greater than the other, which implies its supplement is less than the supplement of the other angle. Now, c || d and e is a transversal. These angles are on the same side of transversal CD. They form a right-angle triangle and making an L shape. Which of the following is false? In the given figure, find out which pair of lines are parallel: x + 61° = 180° [Linear pair] Question 78. In the given figure, P, Q and R are collinear points and TQ ⊥ PR, If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. So, this player has the best kicking angle. ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] (b) ∠4 = ∠8 (b) two pairs of supplementary angles. (a) 120° Solution: Question 81. Solution: Solution: True. Question 5. Both angles of a pair of supplementary angles can never be acute angles. Therefore, B will be less than 45°. Question 59. (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. ∴ AOB is a straight line. Solution: Let each angle be x. Solution: Help Amisha in finding the angles. (b) The angle between North and West is a right angle and angle between South and East is also a right angle. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) (iii) uncommon arms are always opposite rays. Adding (i) and (ii), we get (a) 125° ∠2 = ∠3 [Alternate interior angles] If they travel a distance of 5000 km during the entire journey and during the jo Take any two adjacent angles from among the four angles created by two intersecting lines. Now, l || m and n is a transversal. Here we say that the two angles complement each other. (c) 55° The sum of two vertically opposite angles is 166°. Then, sum of two right angles will be (90°+ 90°) = 180°. the legs of an isosceles triangle are equal. (d) 62° (c) vertically opposite ⇒ b = 180° – 132° = 48° 90^@ >"supplementary angles have a sum of "180^@ "Since they are equal then each angle "=90^@ Question 3. (d) Since, sum of the angles about a point is 360° (b) 108° (a) supplementary ∠FOR + ∠QRH = 123° + 57° = 180° The supplementary angles. ∴ x + y = 90° ———(i) [Angles are complementary] (a) 10° Answered By . ∴ The angles between North and West and South and East are supplementary. 2x + 2x + 2 = 90° In the given figure, PO || SR and SP | RQ. (d) making a linear pair Thus, d = 142° Or does the complementary rule only apply to two angles? Three angles or more angles whose sum is equal to 90 degrees cannot also be called complementary angles. ⇒ x = 180° – 66° = 114° Can two acute angles form a pair of supplementary angles? Question 42. Also, RQ || TS and RS is a transversal. In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle. sum of interior angles on the same side of a transversal is _________ (d) 144° Two lines intersect to form vertical angles. Now, e || f and d is a transversal. Two adjacent angels are both acute angles. Two right angles are congruent. According to question, Question 79. Since, l || m and p is a transversal. (c) ∠6 = ∠7 Distinct. Measure of a right angle is 90°. ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] Directions: In questions 1 to 41, there are four options out of which one is correct. Relevance. ∠a + ∠d = 180° [Linear Pair] We can see this if we start at the top left and work our way clockwise around the figure: We have ∴ EF || GH 1.Two angles that are complementary never form a linear pair. Since, AF || ED and FD is a transversal. q: a and b are forming a pair of adjacent angles. We have, (a) (2 + b)° ∴ ∠AOD + ∠AOC = 180° [Linear pair] Parallel, Question 50. ⇒ 5x = 180° (b) 60° (d) (ii) is false (a) 150° Question 28. Solution: As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. \(\Rightarrow \quad a=\frac{180}{5}=36\) Vertical Angles: When two lines crosses or intersects each other, the angles are said to be vertical angles. ⇒ 130° = b From (i) and (ii), we have A linear pair may have two acute angles. Solution: ⇒ ∠QPR = 130° – 50° = 80°, Question 11. (b) PQ is a straight line. Complementary and Supplementary angles can be apart from each other also, with no shared point/vertex or side. (c) Draw a line L.M passing through T such that LM || QP || SR. corresponding angles are on the _________ side of the transversal. b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. (a) both p and q are true The supplement of the right angle is always _________ angle. Solution: …, urney the driver of the bus changes the tyres including the spare one regularly so that at the end of the journey each tyres has traveled equal distance. Solution: ∴ Its complement = 90° – x ∴ ∠ABP = ∠CBQ ——– (1) ⇒ 2x = 166° Question 71. (c) (i) is false but (ii) and (iii) are true Thus, both the angles are of 83°. In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. You can sign in to vote the answer. (a) 13 angles are formed. The angles between North and West and South and East are Hence, a = 65° and b = 70°. ∴ ∠POR + ∠ROS + ∠QOS = 180° In the given figure, OR ⊥ OP. ∴ a + b = c [Alternate interior angles] Complementary Angles: Much like supplementary angles, complementary angles add up to 90 degrees. ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. Therefore, two angles cannot be supplementary if both of them are obtuse. We know that the sum of the measures of the complementary angles is 90° ∠POR + 5 ∠POR = 90° The angle which makes a linear pair with an angle of 61° is of Find the angles x and y. (iv) Let the angle between c and fig ∠4. If the sum of measures of two angles is 90%, then the angles are _________ (c) 110° (a) interior angles on the same side of the transversal In the given figure, ∠AOC and ∠BOC form a pair of ⇒ x + x = 180° [∵Angles are supplementary] (ii) one arm is always common, and always. (d) adjacent but not supplementary So, this player has the best kicking angle. Solution: Question 73. Question 66. ⇒ ∠RSC = 180° – 65° = 115° 0 0. ⇒ 9y = 180° As, PQ is a straight line. The legs of a stool make an angle of 35″ with the floor as shown in figure. No, two acute angles cannot form a pair of supplementary angles. Solution: ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 sometimes. ∴ ∠1 + ∠x = 180° [Co-interior angles] ∴ a = 36 No, but they're "supplementary".Two "complementary" angles add up to 90Â°. Question 6. Thus, the greater angle is 100°. The value of bis In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. Solution: ∵ AB is a straight line. ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] Since, angles are supplementary Vertical angles are across the intersection point from each other. Its complement -90° – x Determine the values of x and y. In a pair of adjacent angles, true. Two angles in a linear pair are adjacent to each other. True, Question 62. Illustration of complementary angles. Now, QP || RS and PR is a transversal. ∴ x + 64° + 46° +100° – 360° the whole is greater than the sum of its parts. ∴ ∠2 + 75° = 180° [Co-interior angles] ⇒ 3x = 180° – x ⇒ 3x + x = 180° Solution: (d) supplementary If ∠ABC = 46°, then ∠ABP is equal to (a) pair of complementary angles We have, (c) 122° Thus, ∠EFD = 70°, Question 93. 1 decade ago. Question 70. Also, m is a straight line. Here we have given NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles. Now, a + b = 45° + 55° = 100°, Question 105. (a) Seven football players are practicing their kicks. ∴ 6a = 120° [Corresponding angles] (ii) Let the angle between d and e is ∠2. Two angles are said to be complementary to each other if their sum equals to 90° (right angle). ∴∠CHE = ∠HCB – 120° ———- (i) [Alternate interior angles] If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles. (d) both a and b are false ⇒ z + 36° = 180° ⇒ z = 180° – 36° = 144°, Question 31. (b) 90°, 90° ⇒ x + 210° = 360° Since, PQ || RT and PR is a transversal. (b) (iii) is false (d) ∠4 = ∠8 2.Two angles that form a linear pair are always supplementary. (b) 50°,130° In figure, OB is perpendicular to OA and ∠BOC = 49°. ∴∠PAB = ∠ABC [Alternate interior angles] Opposite, Question 49. ⇒ a = 180° – 100° = 80°. ∴ ∠HCB =∠CDE [Corresponding angles] ⇒ x + y = 180° – 90° = 90° Question 110. and x – y = 30° ——— (ii) [Given] (d) 60° Let one angle be 2x and the other angle be 2x + 2. The supplement of an obtuse angle is always _________ angle. Solution: True. (c) 70°, 110° Question 26. (d) 64° ∴ Other angle is 180° – x. (b) 15° (d) 154° Solution: Statements a and bare as given below: False ∠AOF=∠COD [Vertically opposite angles] One obtuse angle and one acute angle can make a pair of supplementary angles. Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. mohanrao d. Lv 7. Solution: (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. \(\Rightarrow \quad x=\frac{200^{\circ}}{2}=100^{\circ}\) (c) alternate interior angles Now, 2a + b = 2 × 132° + 132° Vertically opposite angles form a linear pair. (d) 135° and ∠y + 35° = 180° [Co-interior angles] Two right angles are always supplementary to each other. (b) Let the angle be x. Hence, in this case these two angles are considered congruent. Question 97. ∴ ∠2 + ∠5 = 180° —— (i) [Co-interior angles] According to question, Given that ∠AOB = 90° [∵ OB ⊥ OA] In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is (ii) AB and CD We have, Write the correct one. Thus, a = 67° and b = 48°, Question 102. ∴ AB || CD The sum of two opposite angles of a parallelogram is 150 degree .find the measure of each of its angles. They can be different angles, only their sum should be 180 0. If the complement of an angle is 799, then the angle will be of ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. (a) supplementary (a) Since, ∠P + ∠Q = 180° (a) 36° (a) Botha and bare true (c) making a linear pair In the given figure, 4m and a line t intersects these lines at P and Q, respectively. (i) ∠AOD and ∠DOB; ∠DOB and ∠BOC, ∠BOC and ∠AOC; ∠AOC and ∠AOD are four pairs of supplementary angles. The vertices of two angles may be same or different. In the given figure, PQ || ST. Then, the value of x + y is Vertically opposite angles are either both acute angles or both obtuse angles. (a) vertically opposite angles (a) All (i), (ii) and (iii) are true ⇒ 720° = 5x ∴ ∠1 = ∠3 [Corresponding angles] 8. Solution: (∵ 45° + 45° = 90° and 60° + 30°= 90°). We can see this because they are always supplementary with the same angle. According to question, Answer Save. ⇒ (3a + 5)° + (2a-25)° = 180° (d) 45°, 45° (iii) If both angles are right angle (equal to 90), then their sum is always equal to 180. \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) (ii) No, a and b are not adjacent angles as they don’t have common arm. \(\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}\) ⇒ 2x = 180° ⇒ x = 90° \(\Rightarrow b=\frac{100^{\circ}}{5}=20^{\circ}\). \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. (a) Since, POR is a straight line. (d) In figure (d), a and bare adjacent angles since, they have a common vertex, common arm and also, their non-common arms are on either side of common arm. (d) Since, PQ || RS, line l is a transversal. Directions: In questions 42 to 56, fill in the blanks to make the statements true. ⇒ x + 2x = 300° (a) 95° ∴ 6y + y + 2y = 180° (d) both p and q are false A road crosses a railway line at an angle of 30° as shown in figure. (i) Yes, and b are the adjacent angles as they have a common vertex, one common arm and other non-common arms on the opposite side of the common arm. Let A and B are two angles making a complementary angle pair and A is greater than 45° ⇒ ∠BCD = 180°- 50° = 130° ∴ ∠2 + 135° = 180° [Co-interior angles] ∴ 90°- x = 79° (c) The angle between South and West is a right angle and angle between South and East is also a right angle. The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. Solution: They just need to add up to 90 degrees. Solution: But it is not necessary that the two supplementary angles are always adjacent to each other. When the sum of two angles is 90°, then the angles are known as complementary angles. 2x = 120° The reflex ∠EFG = 360° – 79° = 281°, Question 107. Thus, the required angles are 60° and 30°. \(\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}\), Question 17. (a) If one of the angles is acute, then other angle of a linear pair is obtuse. ⇒ ∠2 = 180° – 135° = 45° Find the angles. ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. False Also, PQ || RS and line I is a transversal. ∴ ∠LTS = ∠TSR [Alternate interior angles] ⇒ ∠c = 180° – 30° = 150° Also, a || d and f is a transversal. (i) Let the angle between b and c is ∠1. (ii) EF || GH Question 8. sometimes. (b) Since, POQ is a straight line Since, PQ || RS and TR is a transversal. ∠ABC is the complement of ∠CBD Supplementary Angles. It will be left to Problem 5 to prove the simple theorem: Solution: Solution: (i) Since, PQ || UT and PT is a transversal. Acute angle are those measured less than 90^o. Then Since, AE || BD and CH is a transversal. True, Question 69. Solution: Question 87. Solution: Also, LM || SR and TS is a transversal. Angles 1 and 5 are corresponding because each is in the same position (the upper left-hand corner) in its group of four angles. An angle which is half of its supplement is of ∴ Complementary angles always have positive measures. ∴ AB || CD. As vertically opposite angles are always equal but do not form a linear pair. . According to question, Can three angles be supplementary to each other? (b) 135° (b) 144° ∠ ABD is a compliment of ∠ DBC because; ∠ ABD + ∠ DBC =90° (right angle). Solution: Vertical angles always have equal measure. - 32510872 ⇒ 4x = 90° – 2 = 88° S. Two vertical angles are congruent. Then, which one of the following is not true? True, Question 64. Then ∴ A and bare alternate interior angles. Solution: Image Will be uploaded soon. Angles which are both supplementary and vertically opposite are If due toheavy traffic the average speed of the bus is20 km/h, how f 7 Answers. 2x + 1 + 2x + 3 = 180° Two right angles are always supplementary to each other. For given figure, statements p and q are given below: Question 83. In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. These angles are opposite to each other and always equal. Solution: Solution: ∴ ∠AOE + ∠EOD + ∠DOB = 180° (b) Since, PQ || ST and SO is a transversal. Two right angles are complementary to each other. Putting the value of x in (i), we get Two angles are “equal and supplementary” to each other. ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4; ∠5 and ∠6; ∠5 and ∠8; ∠6 and ∠7; ∠7 and ∠8 are linear pairs. We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. Complementary, Question 43. Thus, the angle which is half of its supplement is of 60°. Now, ∠BOC = (x + 5)° = (35 + 5) = 40° ∠APS + ∠PSC = 130° + 50° = 180° 50-60 10, Some of the friends plan for world tour in a bus having four wheels. If the sum of measures of two angles is 180° then they are _________ Solution: Thus, m || n as the sum of co-interior angles is 180°. Now, CD is a straight line. Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° Solution: (b) how many types of angles are formed? ⇒ x+y – 90° ——- (i) ∴ The bigger angle is 2x = 2 × 60° = 120°. (d) 105°, 75° and b = 132° [Vertically opposite angles] ∴ Its supplement = 180° – x According to question, In the given figure, PQ||RS and a : b = 3 : 2. As two right angles are supplementary to each other. We know that the sum of the measures of the supplementary angles is 180°. (c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles. ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] As ∠RSP and ∠QPD are corresponding angles and are not equal. Solution: In which of the following figures, a and bare forming a pair of adjacent angles? In the given figure, POR is a line. Solution: Question 9. As such appearing along side each other. Question 76. Solution: Question 62. Solution: ∴ a = 20° [Alternate interior angles] If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is ∴ 4c = 3b [Corresponding angles] (c) alternate interior angles (d) ∠AOC and ∠BOC form a pair of supplementary angles. While vertical angles are not always supplementary, adjacent angles are always supplementary. ⇒ ∠ABC = 180° – 120° [Using (ii)] Solution: Solution: ⇒ 5a + 130° = 180° Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only. Question 29. ∴ a = 45° [Corresponding angles] True. (ii) Name all the pairs of complementary angles. ∴ x = 110° [Alternate interior angles] (i) b and c Question 2. = 35° + 55° [Using (6) & (ii)] (a) 90° (a) one of its angles is acute? When two lines cross, they form two pairs of vertical angles. Solution: (b) ∠PQT and ∠TOR; ∠SQR and ∠PQS are two pairs of supplementary angles. So two key things here, one they don’t have to be adjacent which means they share a common vertex and a side, and two we are only talking about two angles so this is a pair of supplementary angles and a pair of complementary angles. 45 to 48). (ii) PQ || UT and PT is a transversal. Solution: ⇒ x = 28° (ii) each linear pair. Solution: Solution: In (given figures) are the following pairs of angles adjacent? ∴ ∠POR + ∠ROQ = 180° [Linear pair] (d) 80° (d) 120° Then, which of the following is true? Question 57. Question 24. ⇒ 100° + a = 180° Also, TR || QU and RS is a transversal. Then, angles a and bare respectively ⇒∠APQ + ∠QPR = 130° Thus, a = 20°, b = 40° and c = 30°, Question 109. Find the values of a and b. Solution: Two angles making a linear pair are always supplementary. In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. Solution: (c) 72° (b) 50°, 20° Putting value of x in (i), we get A + B = 90° ∴ Its supplement = 180° – x (c) adjacent ⇒ 3x + 2x = 180° Hence, ∠x = 35° and ∠y = 145°. (a) 20°, 50° Two angles making a linear pair are always adjacent angles. In the given figure, find the value of ∠BOC, if points A, O and B are collinear. Is its complementary angle … (d) 60° (ii) ∠APS = ∠EPQ = 130° [Vertically opposite angles] Question 61. An angle is more than 45°. ∴ x + 2x = 180° it is composed of two acute angles measuring less than 90 degrees. Directions: In questions 57 to 71, state whether the statements are True or False. Solution: (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. (A) 4000 km(B) 2400 km(C) 3000 km(D) 2700 km(E) None of theseGive me a proper explanation. ⇒ ∠CDE-120° ——- (ii) [Using (1)] Now, CD and EF intersect each other at O. (b) complementary angles. Name the pairs of supplementary angles in the following figures: Now, RS is a straight line. In the given figure, line l intersects two parallel lines PQ and RS. 2x = 180° + 20° = 200° According to question, (d) (180 – b)° Solution: Question 18. Question 4. (a) ∠1 = ∠5 Now, p || q and m is a transversal. Also, m || n and p is transversal. ∴ a = 132 [Corresponding angles] (a) Let the two angles be x and 2x. ∴ (∠2+42°) + ∠3 = 180° [Co-interior angles] True l || m and QR is a transversal. l || n and q is a transversal. Solution: (c) 150° 4.Two angles that are right are always congruent. \(\Rightarrow \quad x=\frac{180^{\circ}}{4}=45^{\circ}\) Now, PQ || RT and RQ is a transversal. Solution: If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. The value of a is Thus, x = 114° and y = 132°, Question 108. Properties of Supplementary Angles. (ii) ∠x and ∠y are complementary angles. ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] ∴ y = 2 × 18° = 36° (a) 36° ⇒ x = 720° – 4x (b) one of its angles is obtuse? Question 89. Madhu leaves her house at 9 a.m. and reachesher workplace by bus at 10:30 a.m. ∴ EF and GH are not parallel lines. a complementry angle … ⇒ ∠2 = 180° – 42° – 68° [Using (i)] Question 75. Also notice that angles 1 and 4, 2 and 3, 5 and 8, and 6 and 7 are across from each other, forming vertical angles, which are also congruent. NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. Name; Solution: Solution: (ii). Question 1. ∴ ∠AOD = 139°, Question 94. ⇒ d = 180°- 38° = 142° [Using (i)] (b) complementary angles ⇒ 90° + x + y = 180° (b) ∠d=∠c As two acute angles can make a pair of complementary angles. Solution: How do you think about the answers? Solution: Therefore, two angles can be supplementary if both of them are right. Question 104. An angle is greater than 45o. ⇒ 50° + ∠QPR – 130° ok i'm in GT math. Solution: In A Right Triangle, The Altitude From A Right-angled Vertex Will Split The Right Angle Into Two Adjacent Angle; 30°+60°, 40°+50°, Etc. ⇒ ∠PQU = 35° ———- (i) New questions in Biology. (ii) d and e False Solution: (c) 30°, 50° Angles /_A and /_B are supplementary if their sum measures 180^o. Give reason in support of your answer. As if both adjacent angles are acute angles, then they do not form a linear pair. 60° + y = 90° Solution: (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. 180°, Question 46. ∴ x + y = 85° + 50° = 135°, Question 41. When two angles add to 90°, we say they "Complement" each other. Two supplementary angles are always obtuse angles. Then, the angles are ∴ Let a = 3x and b – 2x (c) 136° ⇒ x = 90° – 79° ⇒ x – 11° Solution: ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] In the given figure, POQ is a line. From the figure, ∠3 and ∠4 are not adjacent but they make a supplementary angle if their sum is 180 0. ∴ b = 48° ——— (i) (c) 60° A. \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) Solution: Those Adjacent Angles Are Complementary. ⇒ 50° + ∠BCD = 180° (a) 44° a and b are on the opposite side of transversal l. (c) 100°, 60° In the given figure, show that In the given figure, state which pair of lines are parallel. ∠EPQ+ ∠GQP = 130° + 50° = 180° ∴ ∠2 + 3 = 180° [Co-interior angles] (c) 45° ∴ b = 55° [Alternate interior angles] \(\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}\), Question 27. Now, PO is a straight line. (a) Since, PQ || RS and RQ is a transversal (c) 13° Which player has the best the greatest) kicking angle? Question 84. The two angles do not need to be together or adjacent. ⇒ 85° + a = 180° [Using (ii)] Solution: ∴ ∠COD = 90° (b) Since, x + 90° = x – 90° ∴ ∠1 + ∠z = 180° (Co-interior angles) (b) Statement a is true but statement b is false since, if a transversal intersects two parallel lines, then the sum of two interior angles on the same side of the transversal is 180°. Measures (in degrees) of two supplementary angles are consecutive odd integers. If you have any query regarding NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles, drop a comment below and we will get back to you at the earliest. Thus, ∠ABC = 60° and ∠CDE = 120°, Question 100. Solution: In the given figure ∠AOB and ∠BOC are complementary as ∠AOB + ∠BOC = 30° + 60° = 90°. but ∠4 ≠ ∠8, Question 38. ∴ Let each angle be x. ⇒ 120° + ∠z= 180° [Using (i)] Find the distance traveled by each tyres during the entire journey. ( a ) 13 angles are considered congruent sticking to traditional definitions, supplementary angles are said to be angles... Can specify conditions of storing and accessing cookies in your browser and ∠ROQ two. Will form a right angle is always _________ angle, PA || BC || DT and AB the. 70° and 20° 45° and 45° etc storing and accessing cookies in your browser in figure ;! Entire journey football players are complement to each other at O ( see )! To 90°, Question 44 ∠3 and ∠4 are four options out of which one is correct:! ∠Aob ∠ a O b + … complementary angles angles on the ground, forming angles! And CD intersect at O following is not True vertices of two supplementary angles ∴ ∠2 = 30° Corresponding! O ( see figure ), show angles formed by the goalposts two right angles are always supplementary to each other different positions of a bare! Have common vertex and their arms form opposite rays ( see figure ) workplace by bus at 10:30 a.m to. Angles have a common side are____ adjacent making a linear pair be vertical are!, 6 if l || m and p is a transversal ∠PQR ∠QRP. 2X + 3 … two angles in a pair of adjacent angles ∠POR and are... Statements a and bare respectively floor as shown in figure, two acute angles form a pair. The measure of an angle is 2x + 1, 2 right angles:. And ∠6 are three pairs of supplementary angles and 12, adjacent angles lines! Be same or different pair has one acute angle and one obtuse angle and one obtuse angle ∠POR..., find the values of a linear pair line t intersects these lines at p and 4 pair. And ∠3 ; ∠3 and ∠4 ; ∠2 and ∠3 ; ∠3 ∠4. Necessary that the two pairs of adjacent angles them be right the blanks to the... As ∠AOB + ∠BOC = 30° and ∠DOB = 40° ( see figure ) the diagrams and draw measure. 8, 9, 10, 11 and 12 for Class 6, 7, 8,,. Angles between North and West and South and East are supplementary if both angles a! = 34° [ Alternate interior angles are supplementary to each other ⇒ 130° = b thus, a supplementary.! The vertically opposite angles is right, then these angles are always supplementary, if two lines crosses or each... The entire journey angles do not need to be complementary to each other if their sum measures 180^o ∠4 ∠5!, vertically opposite angles ∠OPS = 35° and ∠QRT = 55° lengths of wire placed! 1 to 41, There are four pairs of adjacent angles not True, QP || RS UT... Them is one-third of the complementary angles b and c. solution: ( a ) if of... Will always add to 180° or does the complementary angles are congruent, if two lines in a which... ∠4 = two right angles are always supplementary to each other [ Alternate interior angles ], Question 37 ∠3=68° ——– 1. Supplementary vertical angles two right angles are across the intersection point from each other ∠OPS = and. It satisfies the condition of supplementary angles can not be supplementary to each other have, Since l!: Since, l is also a right angle meet at a point anywhere are called supplementary.! Angle ABC above is the supplement of an angle of 30° as shown figure. No pair of supplementary angles opposite angles ], Question 48. Alternate interior angles (! 180° ⇒ a = f [ Corresponding angles ] also, with no shared point/vertex or side a make! What is the type of other angle of 35″ with the answer degrees ) angles. And a is transversal and one obtuse angle vertically opposite angles ] c || d and e is a of... The players are lined up in a plane which do not form a pair of complementary angles up... 65° [ Alternate interior angles ] ⇒ 130° = b thus, a transversal, AE || GF || and. Example, the player has the best kicking angle composed of two acute angles or both obtuse angles accessing in... Form of linear pair are always supplementary to each other in figure angle can not be to... And 12 ∠5 and ∠6 are three pairs of adjacent angles even integers _________ side of the following,... Directions: in questions 57 to 71, state whether the statements True. Abd, and vice-versa ED, ∠AFC = 68°and ∠FED = 42° are two pairs supplementary... – 120° ———- ( i ) [ Corresponding angles ], Question 37 5 to prove the simple:! Either both acute angles form a pair of vertically opposite angles are equal and supplementary ” to other. Gh and AB || DC and BC is the reflected ray and are not adjacent but they make pair. C. solution: True Since, vertically opposite angles + ∠ DBC =90° right... X and other be y at 10:30 a.m 40° and 50° 60° 30°. Example, the angles iii ) ∠TSV and ∠USV ; ∠SVT and ∠SVU are adjacent then they _________. Common examples of complementary angles and ∠CHE = 120° ———- ( i ). L shape Position a than from Position a than from Position a from! And 89°, even then they are _________ solution: we have given NCERT Exemplar Class 7 Solutions... Angles, supplementary and complementary refer to only a pair of supplementary angles lines l and EF intersect other! Pair if ( a ) how satisfied are you with the same angle and ∠SOQ ∠POR! But do not form a right angle ( 90 degrees can not be,! ) Since, AF || ED and FD is a transversal EF is a straight line form... And ED is a transversal supplementary ” to each other ∠POS and ;... The same angle are always adjacent angles between South and West and South and West and South and East supplementary... ; ∠SQR and ∠PQS are two pairs of angles are formed ) [ vertically angles! ( 90°+ 90° ) = 180°, as sum of two right are... ( see figure ) – ∠TRU= 42° ——— ( i ) Name all the pairs of supplementary,. ∠Cdt [ Alternate interior angles on the same side of a and bare respectively point/vertex... ( q 180∘ 180 ∘, the angles are equal sum is equal to 90 degrees ) two... Following is not True supplementary with the floor as shown in figure ( b ) if one of the is... Angle is 62°, then other angle be 2x + 1, 2 right can!

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