⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 Two angles making a linear pair are always supplementary. Its complement -90° – x Solution: Question 42. Solution: ⇒ ∠Q = 180° – 60° = 120°, Question 13. (i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles. (a) 10° (b) supplementary In which of the following figures, a and bare forming a pair of adjacent angles? (d) 45°, 35° (d) 135° ∴ EF || GH (a) alternate exterior angles (i) ∠PSC = ∠RSF = 50° [Vertically opposite angles] Since, PQ || RS and TR is a transversal. (c) p is false and q is true (ii) EF || GH Thus, a = 67° and b = 48°, Question 102. (a) 110° (d) equal Since, AB || l and EF is a transversal. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) If the sum of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together.Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together. (d) 62° Question 30. Complementary angles are two angles that have a sum of 90°. ⇒ 720° = 5x (d) making a linear pair ∴ Its supplement = 180° – x In the given figure, if QP || SR, the value of a is In the given figure, POQ is a line. Thus, x = 114° and y = 132°, Question 108. Therefore, B will be less than 45°. Directions: If a transversal intersects two parallel lines, then answer (Q. ⇒ 4 × 30° = 3b      [using (i)] (iii) d and f Solution: 90°, Question 55. ⇒ z + 36° = 180° ⇒ z = 180° – 36° = 144°, Question 31. Solution: ⇒ B = 90° – A (ii) ∠x and ∠y are complementary angles. (d) 60° Yes, because the sum of two angles is 180, and if they are both 90 degrees, they add up to 180, making them supplementary, and of the same measure, making them congruent. Solution: ⇒ f = 108°, Question 37. 2. Complementary Angles. Try These: Question 1: Which pairs of following angles are complementary? ∴ b = 50° [Alternate interior angles]. ⇒ b = c – a Question 86. ⇒ ∠QUR = 180° – 42° = 138°. Solution: Solution: Amisha makes a star with the help of line segments a, b, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in figure, and asks Amisha to find the ∠x, ∠y and ∠z. Then, Solution: Putting value of x in (i), we get Find the values of a, b and c. One angle of a pair of complementary angles is given. Now, AB || CD and ED is a transversal. ⇒ ∠BCD = 180°- 50° = 130° We have because 90° + 90° = 180°, as it satisfies the condition of supplementary angles. A supplementary angle makes a straight line. \(\Rightarrow b=\frac{100^{\circ}}{5}=20^{\circ}\). (a) 120° But the angles don't have to be together. (b) how many types of angles are formed? In the given figure, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y. (c) Draw a line L.M passing through T such that LM || QP || SR. (c) 20° Solution: but ∠2 + ∠3 = 180°, Question 39. ⇒ 2x = 180° ⇒ x = 90° ∴ 90°- x = 79° In the given figure, ∠AOC and ∠BOC form a pair of ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] (d) both are obtuse In the given figure, POR is a line. Therefore the two smaller ones must add to 90° and so are complementary by definition). Solution: Easy measure angles, using interactive whiteboard angle simulator. ⇒ 60° + ∠2 = 180° [Using (ii)] As, PQ is a straight line. Yes, 2 right angles can form a supplementary angle. If two angles add up to 90°, they are _____ angles. (b) 50°, 20° Solution: ⇒ ∠RQU = 35° ——- (ii) In the given figure, if PQ || RS and QR || TS, then the value of a is Find the measures of two complementary angles if one angle is five times the other angle. Solution: Solution: \(\Rightarrow \quad a=\frac{120^{\circ}}{6}=20^{\circ}\) In the given figure, 4m and a line t intersects these lines at P and Q, respectively. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] Find the angles x and y. Using the reflex angle, we can find the measure of the acute angle. Take any right angle and draw in a ray that has its endpoint as the vertex of the right angle. Solution: = 60° 60°: Let the angle be x. Measures (in degrees) of two complementary angles are two consecutive even integers. Question 85. Solution: (b) 15° Solution: Determine the values of x and y. (d) Since PQ I RS and line 1 is a transversal. Such angle pairs are called a linear pair. (b) Since, PA || BC and AB is a transversal. (iii) uncommon arms are always opposite rays. (d) adjacent but not supplementary 2x = 180° + 20° = 200° (a) 125° Let one angle be x. The measure of an angle's supplement is 44 degrees less than the measure of the angle. ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] Solution: (d) supplementary Solution: (a) Since, ∠P + ∠Q = 180° (a) both p and q are true ∴ A and bare alternate interior angles. In a pair of adjacent angles, (b) 100° Solution: (b) complementary angles (a) Botha and bare true (c) 80° ⇒ 30° + 5y = 180° Since sum of the these two angles are 90 o (d) 105°, 75° ∴ y + 48° = 180° [Co-interior angles] If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) ∴ Its supplement = 180° – x Now, EF || GH and AB is a transversal. 4.Two angles that are right are always congruent. Add your answer and earn points. In the given figure, line l intersects two parallel lines PQ and RS. Solution: ∴ 6y + y + 2y = 180° A supplementary angle usually involves two angles that are adjacent and adds up to 180 degrees. Solution: Solution: Two angles making a linear pair are always adjacent angles. (c) 64° (d) supplementary angles If the two complementary angles are adjacent, their non-shared sides form a right angle. ∴ ∠x = 35° [Alternate interior angles] In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is The two angles, say ∠X and ∠Y are complementary if, ∠X + ∠Y = 90° In such a condition ∠X is known as the complement of ∠Y and vice-versa. An angle which is half of its supplement is of ∴ We know that the sum of the measures of the supplementary angles is 180°. corresponding angles are on the _________ side of the transversal. Since, l || m and AB is a transversal. A transversal intersects two or more than two lines at _________ points. (b) 11° Thus, one angle is 89° and other is 91°, Question 99. (d) ∠3 = ∠7 (a) supplementary As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary (b) 50° ∴ ∠POQ + ∠QOR = 180° [Linear pair] Now, c || d and e is a transversal. Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. and ∠y + 35° = 180° [Co-interior angles] ⇒ ∠c + 30° = 180° [Using (iii)] ⇒ 3x = 180° A pair of complementary angles is angles . (c) 16° (b) one of its angles is obtuse? ∴ Its complement = 90° – x Justify your answer. (c) (108 – b)° Solution: No, two acute angles cannot form a pair of supplementary angles. Example 2: 60°+30° = 90° complementary and adjacent Example 3: 50°+40° = 90° complementary and non-adjacent (the angles do not share a common side). (c) 85° Acute, Right, Obtuse, Straight, Reflex & Complete angle. False Then, the values of a and bare respectively. When talking about complementary angles, it's important to remember that they're always in apair. Solution: In the given figure, PQ || ST. Then, the value of x + y is ∴ a = 20° [Alternate interior angles] Thus the required angles are 90° each. If two supplementary angles are in the ratio 1 : 2, then the bigger angle is The C in complementary can be used to form the 9 in 90. (a) ∠1 = ∠5 As angles ∠QRS and ∠CSR are alternate interior angles and are equal. Solution: add up to 90 degrees(a Right Angle ). 45° : Given, angle = 45° In the given figure, PO || RS. ∴ Let a = 3x and b – 2x ∴ ∠1 + ∠5 = 180° [By(i)and(iii)] In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. 2x + 1 + 2x + 3 = 180° We know that when the measure of an angle is exactly 90°, then it is known as a right angle. (b) Since, PQ || ST and SO is a transversal. ⇒ ∠z = 180° – 120° = 60° There is an easy way to try and remember these using the first letters of each word. Now, l is a straight line. In the given figure, line l intersects two parallel lines PQ and RS. ∠EPQ+ ∠GQP = 130° + 50° = 180° From (i) and (ii), we have (c) 136° ⇒ 50° + ∠QPR – 130° Find the value of a + b. Find the reflex ∠EFG. Two lines in a plane which do not meet at a point anywhere are called _________ lines. ⇒ 5b – 180° – 80° = 100° \(\Rightarrow \quad x=\frac{210}{6}=35\) They just need to add up to 90 degrees. ∴ ∠2 + ∠5 = 180° —— (i) [Co-interior angles] ∠POR + 5 ∠POR = 90° They are lined up in a straight line in front of the goalpost [See fig.(i)). Hence, two right angles are never be complementary. ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 Solution: Thus, the angle which is half of its supplement is of 60°. 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(d) 75° ⇒ x = 180° – 61° = 119° but ∠a ≠ ∠d, Question 12. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) (c) Since, AB || CD and PR is a transversal Supplementary angles and complementary angles are defined with respect to the addition of two angles. (b) (iii) is false Now, a || d and c is a transversal. Solution: True, Question 64. Directions: In questions 42 to 56, fill in the blanks to make the statements true. (b) 61° Find each of the angles. p: a and bare forming a linear pair. Help Amisha in finding the angles. (d) both p and q are false Learn how to define angle relationships. (b) 24° ⇒ 2∠ABP = 180° – 46° = 134 ⇒ 50° = a (ii) ∠APS = ∠EPQ = 130° [Vertically opposite angles] Online protractor or angle problems with acute, obtuse, reflex angles. Solution: In the given figure, write all the pairs of supplementary angles. ∴ y + 80° = 180° [Co-interior angles] (a) 36° Question 79. Solution: Since, 90° + 90° = 180°, a supplementary angle. Arm, Question 47. (c) making a linear pair Now, p || q and n is a transversal. 45 to 48). Question 2. \(\Rightarrow \angle A B P=\frac{134^{\circ}}{2}=67^{\circ}\). ∵ AB is a straight line. An angle is more than 45°. Question 45. ⇒ 3a – b = 180 – 2a – b Also, BC || DT and DC is a transversal. (b) Now the players are lined up as shown in Fig. Right, Question 53. Solution: In the given figure, line I intersects two parallel lines PQ and RS. (d) Since, sum of the angles about a point is 360° According to question, Its complementary angle will be _________ (d) (180 – b)° Solution: (c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles. Also, m || n and QR is a transversal. \(\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}\) complimentary angles add up to 90 and a right angle is 90 degrees so the answer is always. Give reason. (c) ∠a + ∠d = 180° \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. (c) a is false and b is true Since, l || m and is a transversal. ⇒ x = 360° – 2x – 60° Thus, ∠EFD = 70°, Question 93. z + y = 180° [Linear pair] (b) Given that a : b = 3 : 2 a and b are on the opposite side of transversal l. Vertically opposite angles are always Solution: In the given figure, P, Q and R are collinear points and TQ ⊥ PR, In the given figure, PO || SR and SP | RQ. Example: From the above example ∠POR = 50 o, ∠ROQ = 40 o are complementary angles. ⇒∠APQ + ∠QPR = 130° A road crosses a railway line at an angle of 30° as shown in figure. ⇒ x = 28° Solution: Proof Solution: (a) ∠1 = ∠3 (d) 45°, 45° Find the angles. Two Angles are Supplementary when they add up to 180 degrees. One obtuse angle and one acute angle can make a pair of complementary angles. 2x + 2x + 2 = 90° Let one angle be 2x and the other angle be 2x + 2. (a) 35° (d) Let the angle be x. ∴ ∠2 = ∠6= (34 – b)° ——– (i)[Corresponding angles] It will produce the same result. Question 28. Complementary angles are always in a pair. No, two acute angles cannot form a pair of supplementary angles. (a) 100° 2 See answers profantoniofonte profantoniofonte Answer: … ⇒ x = 180° – 66° = 114° In a pair of complementary angles, each angle cannot be more than_____. ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) (b) ∠2 = ∠4 Question 85. ∠a + ∠d = 180° [Linear Pair] ∴ Angles between South and West and South and East are making a linear pair. Solution: (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. ∴ ∠5 = ∠8 [Alternate interior angles], Question 40. Find ∠ABC and ∠CDE. (c) If one of the angles is right, then other angle of a linear pair is also right. Now, RS is a straight line. (a) supplementary And that is because their measures add up to 90 degrees. (b) ∠PQT and ∠TOR; ∠SQR and ∠PQS are two pairs of supplementary angles. False Explanation: Angle equal to 90 o is called right angle. Question 6. The value of bis 45° _____ 4. ⇒ 5x = 180° For example, the player has a better chance of scoring a goal from Position A than from Position B. (b) 60° ⇒ 5a + 130° = 180° (a) 60°, 120° ∠1 = 120° ———- (i) [Vertically opposite angles] (a) 20°, 50° Question 78. Now, a + b = 180° [Angles on a straight line PQ] Solution: ⇒ ∠AOD = 180°- 41° [Using (1)] 0 0. (d) 154° (d) (ii) is false and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° Also, m || n and p is transversal. If the complement of an angle is 62°, then find its supplement. ∴ ∠HCB =∠CDE [Corresponding angles] The greater the angle, the better chance the player has of scoring a goal. (i) EF and GH (a) All (i), (ii) and (iii) are true Also, PQ || RS and line I is a transversal. We have, Question 35. Solution: Now, e || f and c is a transversal. This site is using cookies under cookie policy. Measures (in degrees) of two supplementary angles are consecutive odd integers. Write the correct one. (c) ∠6 = ∠7 (i) AB || CD We have, (c) 30° Since  ∠AOC and ∠BOC have a common vertex O, a common arm OC and also, their non-common arms, OA and OB, are opposite rays. If the two complementary angles are adjacent then they will form a right angle. ∴ The angles between North and West and South and East are supplementary. So, this player has the best kicking angle. Question 77. (c) 20°, 50° 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. ∴ x + 2y + 3y = 180° If the sum of two angles are 90 o then the angles are said to be Complementary angles. If two angles have a common vertex and their arms form opposite rays (see figure). In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. Find ∠EFD. In a right triangle, the two smaller angles are always complementary.(Why? ⇒ 3x + 2x = 180° (a) ∠a = b The S in supplementary can be used to form the 8 in 180. Question 59. Question 8. If the sum of measures of two angles is 90%, then the angles are _________ Solution: \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) (i) Name all the pairs of adjacent angles. Complementary angles are two angles whose measures add to 90°. ⇒ ∠2 = 180° – 75° = 105° (b) ∠4 = ∠8 (ii) No, a and b are not adjacent angles as they don’t have common arm. As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. Three angles or … Question 97. Question 3: Can two right angles complement each other? (c) 90° Recall that the complementary angle is one that makes the given angle become 90°. Question 87. (a) 30° The angle The angles x and 90° – x are ∴ ∠PQT = ∠LTQ [Alternate interior angles] A right angle measures 90°. ⇒ 9y = 180° Find the angles. The supplement of an acute is always _________ angle. ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. (ii) EF is a straight line. (d) 120° Thus, ∠ABC = 60° and ∠CDE = 120°, Question 100. (b) a is true and b is false \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) (d) 30° An obtuse angle measures greater than 90° and less than 180°. and x – y = 20° ——— (ii) [Given] Solution: (a) 13 angles are formed. (d) 144° 1 answer. (c) The angle between South and West is a right angle and angle between South and East is also a right angle. Now, a + b = 45° + 55° = 100°, Question 105. (a) how many angles are formed? (c) ∠5 = ∠8 ⇒ 4x = 90° – 2 = 88° Which player has the best kicking angle? ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] ⇒ 5 ∠POR = ∠QOS ——– (ii) Complementary angles are those whose sum is equal to 90°. And just as another point of … As if both angles are 89° and 89°, even then they cannot make the sum 180°. (i) b and c ∴ The bigger angle is 2x = 2 × 60° = 120°. 3k + 2k = 90° ⇒ 5k = 90° The angles between North and West and South and East are \(\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}\), Question 27. Angles between South and West and South and East are What is the type of other angle of a linear pair if From (i) and (ii), we get (a) Let an angle be x. ⇒ ∠2 = (3 × 36 – b)° = (108 – b)°, Question 36. D. a supplementary angle. (b) In a pair of adjacent angles, vertex is always common, one arm is always common and their non-common arms are on either side of the common arm. ⇒ ∠COA – 41° ——— (i) B. a right angle. Solution: ∠2 = ∠4 [Corresponding angles] ⇒ a = 67° a = ∠1 + ∠2 = 60° + 30° = 90°. q: a and b are forming a pair of adjacent angles. Thus, the required angles are 60° and 30°. (b) 15° Then, which of the following is true? ⇒ x + 210° = 360° Solution: ⇒ 60° – ∠L ——— (i) ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] Question 18. Solution: We know that the sum of the measures of the complementary angles is 90° Solution: As if both angles are 89° and 89°, even then they cannot make the sum 180°. ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] We have, In the given figure, find the value of ∠BOC, if points A, O and B are collinear. Solution: According to question, 3.Two angles that are congruent are sometimes right. Now, l || m and p is a transversal. (b) 50°,130° Now, PQ || RS and PR is a transversal. \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) True, Question 63. In the given figure, lines and m intersect each other at a point. (c) If one of the angles is right, then other angle of a linear pair is also right. Solution: Solution: ADC and BDC are . (d) Since, PQ || RS, line l is a transversal. ∴ ∠LTS = ∠TSR [Alternate interior angles] Solution: (d) 80°,100 ∴ a = 36 [ ∵∠AOE = 30° and ∠DOB =40° (given)] Solution: Question 84. (d) 64° So the measure of angle DBA plus the measure of angle ABC is equal to 90 degrees. Also, m is a straight line. (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. Question 70. (d) We have, ∴ (∠2+42°) + ∠3 = 180° [Co-interior angles] As vertically opposite angles are always equal but do not form a linear pair. If x= 30°, then ∠QOR is Solution: Thus, a = 50° and b = 130°. In this example, let's put some Algebra to work to find the measure of two angles whose sum equals 90 degrees, better knows as complementary angles. (b) The angle between North and West is a right angle and angle between South and East is also a right angle. According to question, Complementary angles: Two angles that add up to 90° (or a right angle) are complementary. ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) (c) 60° We have, In the given figure, if l || m, find the values of a and b. Solution: In a right angle triangle, as the measure of the right angle is fixed, the remaining two angles always form the complementary as the sum of … 2.Two angles that form a linear pair are always supplementary. ∴ These angles are complementary. In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. Ex. What is the measurement of the other angle? Solution: Question 66. Since, l || m and q is a transversal ⇒ 6 ∠POR = 90° Since, AF || ED and FD is a transversal. ∴ ∠RSC + ∠CSF = 180° [Linear pair] Solution: ∴ b + 132° = 180° [Co-interior angles] and its supplement = 180° – x= 180°- 100 = 80° The difference of two complementary angles is 30°. Also, a || d and f is a transversal. ∴ ∠PQR + ∠RQO = 180° [Linear pair] Solution: If two angles add up to 180o they are _____ angles. How do you think about the answers? (e) Since, POQ is a straight line. In the given figure, the value of x is Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] Now, l || m and n is a transversal. Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. Now, PO is a straight line. An acute angle measures greater than 0° and less than 90°. ∴ a = 132 [Corresponding angles] Solution: Now, CH || DF and CD is a transversal. ⇒2x = 180° – x ⇒ ∠2 = 180° -60° = 120° (b) PQ is a straight line. When talking about complimentary angles, always remember that the angles appear in pairs. The Right angles can make a pair of complementary angles- _____ 1 See answer Kyuvaraj1034 is waiting for your help. (c) 5° Solution: Acute, Question 54. Question 75. Solution : False Measure of right angle is 90°. Question 82. You can specify conditions of storing and accessing cookies in your browser. Thus, one angle is 100° and other is 80°. The reflex angle can be calculated if the measure of the acute angle is given, as it is complementary to the acute angle on the other side of the line. (c) one of its angles is right? ∠APS + ∠PSC = 130° + 50° = 180° ⇒ 90° – 62° = x Solution: and ∠1 = 30°[Vertically opposite angles] (c) both are acute ∴ ∠QRT = ∠RQU [Alternate interior angles] Solution: Given that \(\frac{x}{y}=\frac{3}{2}\) Solution: Find ∠QUR. Question 24. ⇒ 5b + 2 × 40° = 180° In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. x = 2(180° – x) – 60° c || f and a is transversal. ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] Two angles are making a linear pair. ∴ x + 66° = 180° [Co-interior angles] (a) Let the two angles be x and 2x. (b) Let the angle be x. (c) vertically opposite (d) 22.5° Solution: (b) 80° (c) Since, angles are on a straight line. The result will be a pair of adjacent complementary 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°. Also, TR || QU and RS is a transversal. (b) complementary angles. Recall that two angles are complementary if the sum of their measures is​ 90°. Question 32. \(\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}\) (b) Since, POQ is a straight line there was a theft in the temple and two houses were broke up. (c) 55° ∠d = ∠c [Vertically opposite angles] What is a Complementary Angle? asked Jun 2 in Lines and Angles by Subnam01 (52.0k points) lines and angles; class-7 ; 0 votes. Use on interactive whiteboards, angles can be automatically shown or measured with a protractor. Given that. when the owners were awa ⇒ y = 90° – 60° = 30° EASY. (d) 20° ∴ ∠b + ∠1 = 180° [Linear pair] Here we have given NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles. False. In figure, OB is perpendicular to OA and ∠BOC = 49°. ⇒ 4x = 180° (d) 90° In the given figure, two parallel lines l and m are cut by two transversals p and 4. ⇒ a = 180° – 85° = 95°. Let each angle be x. ⇒ 50° + ∠BCD = 180° Question 25. Now, SP || RQ and PR is a transversal. ⇒ ∠1 = 70° [Using (ii)] ⇒ 3x = 180° – x ⇒ 3x + x = 180° Solution: Then, f is equal to In the given figure, the value of y is True, Question 65. Also, p || q and l is a transversal. (i) toon(iii)up​, explain various security standards for internet​. One obtuse angle and one acute angle can make a pair of complementary angles. If two angles are complementary of each other, then angles add up to form 9 0 degree. (b) ∠d=∠c If two angles are complementary of each other, then each angle is: A. an obtuse angle. (a) 60°, 30° = 264° + 132° = 396°. Which player has the best the greatest) kicking angle? The supplement of the right angle is always _________ angle. ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] (d) 60° Three lines AB, CD and EF intersect each other at O. ∴ ∠1 = ∠3 [Corresponding angles] ⇒ x + x = 180° [∵Angles are supplementary] Solution: Find ∠AOD. 2. Question 104. Both angles of a pair of supplementary angles can never be acute angles. Solution: Solution: ∴ AOB is a straight line. Distinct. (c) 100°, 60° Opposite, Question 49. Now, l is also parallel to CD and FG is a transversal. Question 83. 4 years ago. Sum of two right angles is 180° which is double the sum of two complementary angles. Complementary, Question 43. Can two acute angles form a pair of supplementary angles? x + 61° = 180° [Linear pair] ⇒ x + 4x = 720° ⇒ x = 720° – 4x ⇒ y = 180° – 48° = 132° In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. Reflex Angle. ∠2 = ∠3 [Alternate interior angles] A + B = 90° The value of a is ∴ b = 48° ——— (i) In this construction you can extend either leg back. They can be adjacent angles but don’t have to be. Thus, a = 20°, b = 40° and c = 30°, Question 109. (b) 90° \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) False Solution: Now, 60° + ∠1 = 60° + 120° = 180° and these angles are interior angles on the same side of transversal l. Solution: l || m and QR is a transversal. ∴ a = 65° [Alternate interior angles] ⇒ ∠b = 180° – 30° = 150° [Using (1)] ∠6 = ∠7 [Alternate exterior angles] Question 5. ∴ (a + b) + 65° = 180° [Co-interior angles] Question 3. (d) 119° (a) one of its angles is acute? (a) 5b + 2a = 180° [Linear pair] (c) 45° ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 ⇒ 2x = 166° ∴ ∠3=68° ——– (i) [Corresponding angles] ∴ Let each angle be x. Write down each pair of adjacent angles shown in the following figures: ⇒ ∠2 = 180° – 42° – 68° [Using (i)] In the given figure, PA || BC || DT and AB || DC. (i) Let the angle between b and c is ∠1. (c) PQ || RS, line l is a transversal. Solution: Putting the value of x in (i), we get ∴ ∠2 = 30° [Corresponding angles] There's also a word for two angles whose sum add up to 90 degrees, and that is complementary. \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. Since, AE || BD and CH is a transversal. According to question, ∴ AB and CD are not parallel lines. From (i) and (ii), we get What are the measures of the angle and its supplement? ⇒ 130° + y = 180° a: If two lines intersect, then the vertically opposite angles are equal. (d) 120° Knowledge of the relationships between angles can help in determining the value of a given angle. Which of the following is false? (a) 150° Question 72. ∴ 2x = 2 × 22° = 44° and 2x + 2 = 44° +2 = 46° It is just a complete one angle. If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is Question 61. ∴∠PAB = ∠ABC [Alternate interior angles] (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. Solution: An angle is 45°. (b) ∠2 + ∠5 =180° Then, which one of the following is not true? Two right angles are complementary to each other. The two angles do not need to be together or adjacent. Solution: ∴ Its supplement = 180° – x Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° (d) 10° ⇒ x+y – 90° ——- (i) Now, CD and EF intersect each other at O. Question 60. Thus, ∠COF = 110°, Question 95. The supplement of an obtuse angle is always _________ angle. Solution: Supplmentary angles are two angles whose measures add to 180°. (c) write all the pairs of vertically opposite angles. ⇒ ∠ABC = 180° – 120° [Using (ii)] (i) vertex is always common, Solution: We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. - one angle is 90° and all three add up to 180°. 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