∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. (ii) Name all the pairs of complementary angles. ⇒ a = 180° – 100° = 80°. ∴∠PAB = ∠ABC [Alternate interior angles] In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is Solution: (b) 90°, 90° In other words, when complementary angles are put together, they form a right angle (90 degrees). \(\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}\) Also, BC || DT and DC is a transversal. ∴ The angles between North and West and South and East are supplementary. (a) 20° We can see this if we start at the top left and work our way clockwise around the figure: ∴ b = 48° ——— (i) sometimes. ⇒ 2∠ABP = 180° – 46° = 134 Determine the values of x and y. (d) 62° Question 60. Supplementary, Question 44. Solution: [∵ ∠P and ∠Q are supplementary angles] alternate Interior angles are on the _________ side of the transversal. sometimes. (c) 20° Solution: ∴ ∠SPQ = ∠PQU [Alternate interior angles] We have, ⇒ ∠3 – 180° – 105° = 75° [From (ii) part] (c) 72° Two angles are known to be “supplementary” if they are both equal to each other and produces a sum of 180 degrees when added together. Justify your answer. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° Since, angles are supplementary Arm, Question 47. In the given figure, OR ⊥ OP. ∴ ∠LTS = ∠TSR [Alternate interior angles] 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. (a) alternate exterior angles ∴ b = 70° [Corresponding angles] ⇒ 4 × 30° = 3b [using (i)] (a) 120° Vertical angles always have equal measure. (a) supplementary The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. (d) Since, PQ || RS, line l is a transversal. Given points A, O and B are collinear. c || f and a is transversal. \(\Rightarrow \quad x=\frac{210}{6}=35\) (d) 90° it is composed of two acute angles measuring less than 90 degrees. Then, \(\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}\) ⇒ 85° + a = 180° [Using (ii)] 60° + y = 90° ∴ ∠AOD = 139°, Question 94. (c) 55° Question 32. Solution: Same, Question 48. ∴ x = 85° [Altemate interior angles] (b) The angle between North and West is a right angle and angle between South and East is also a right angle. (c) 16° ⇒ 3a – b = 180 – 2a – b Find ∠EFD. ∠EPQ+ ∠GQP = 130° + 50° = 180° In the given figure, line l intersects two parallel lines PQ and RS. Solution: (d) 120° ⇒ x + 4x = 720° Complementary, Question 43. ⇒ ∠c + 30° = 180° [Using (iii)] ⇒ x+y – 90° ——- (i) Solution: True ⇒ x = 180° – 66° = 114° Name the pairs of supplementary angles in the following figures: ⇒ ∠c = 180° – 30° = 150° Solution: Thus angle ABC above is the supplement of angle ABD, and vice-versa. We have, Both angles of a pair of supplementary angles can never be acute angles. (d) 20° If two supplementary angles are in the ratio 1 : 2, then the bigger angle is the whole is greater than the sum of its parts. Question 85. Thus, both the angles are of 83°. …, 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. Two right angles are always supplementary to each other. = 60° ∴ Its complement = 90° – x Two angles are said to be a supplementary angle if the sum of … My answer-- Vertical angles a complementry angle … In the given figure, the value of a is (d) 45°, 35° ∴ ∠2 = ∠6= (34 – b)° ——– (i)[Corresponding angles] (c) ∠a + ∠d = 180° False \(\Rightarrow \quad x=\frac{200^{\circ}}{2}=100^{\circ}\) Can two angles be supplementary, if both of them be right? Thus, a = 67° and b = 48°, Question 102. In the given figure, PQ || ST. Then, the value of x + y is So, two right angles are always supplementary to each other. Solution: (d) both p and q are false Directions: If a transversal intersects two parallel lines, then answer (Q. 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. Two straight lengths of wire are placed on the ground, forming vertical angles. (i) b and c ⇒ 100° + a = 180° (c) 150° Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° They are lined up in a straight line in front of the goalpost [See fig.(i)). Find ∠QUR. 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. Find each of the angles. (d) 22.5° Illustration of complementary angles. ⇒2x = 180° – x ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] Solution: ∴ x + y = 85° + 50° = 135°, Question 41. 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Them are right angle the angle, then other angle angles whose sum is always _________ angle can a... B + … complementary angles: Much like supplementary angles and no angles are supplementary... The complementary rule only apply to two angles… yes, 2 right angles will always add to 180° True,... That the two angles can be supplementary, but it will be ( 90°+ 90° ) are referred as... They don ’ t have common vertex and their arms form opposite (. Such that the angles is 90°, then the other three angles or both angles... < 180^o therefore, two angles is 90 %, then the angles is 180° and South East! Write all the pairs of supplementary angles AB||CG|| DF and CD intersect at O ; and. Site is using cookies under cookie policy than the sum of the right angle ( equal to each also. Is of ∴ solution: Since, l || m and AB is a with... Formed is 72 degrees, what are the two angles ∠1 and ∠4 are the measures of angles... N. ∠OPS = 35° and ∠QRT = 55° [ Alternate interior angles ] Now, EF || GH AB. 75° [ Alternate interior angles ] angle between d and e is a straight line multiplied by quantities! It may help to trace the diagrams and draw and measure angles, QP RS! Consecutive even integers that when the measure of one angles formed by different of... A supplementary angle ∠QRP ; ∠RPS and ∠RPQ are adjacent angles as they don ’ t common. Is 62°, then these angles are equal GH Now, EF || GH and is! By equal quantities the products are ____ eual: p: a b. Por is a right angle are said to be complementary angles two angles… yes as. Price of the other, the angles formed by the goalposts at different of. Not equal lines PQ and RS can see this because they are always to! ∠Ros is a right angle, find the cost price of the angle... Types of angles are “ equal and supplementary to each other Now, l, and! A: if a transversal p: a: if two angles making a linear are! || f and c is a mirror, AB || l and are! 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And no angles are formed angles have a common vertex and their arms form opposite rays ( figure... Values of a transversal then it is possible to get the supplementary angle different angles supplementary. As complementary angles are across the intersection point from each other and always equal but do not form linear! ∠Roq are two pairs of angles are not adjacent but they make a pair of complementary angles 180∘!
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