…, 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. In the given figure, PA || BC || DT and AB || DC. ∴ x + y = 180° ———– (i) (a) Let an angle be x. Find the angles x and y. ⇒ 5y = 180° – 30° = 150° Two lines AB and CD intersect at O (see figure). 2.Two angles that form a linear pair are always supplementary. $$\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}$$ Now, PQ || RS and PR is a transversal. ∠a + ∠d = 180° [Linear Pair] Question 35. (d) 119° (d) Since, PQ || RS, line l is a transversal. Solution: (a) 35° (c) adjacent (a) vertically opposite angles (b) 4th player has the greatest kicking angle. According to question, (c) ∠6 = ∠7 ⇒ 130° + y = 180° ⇒ b = 180° – 132° = 48° Which of the following is false? In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. Vertical angles always have equal measure. ∴∠CHE = ∠HCB – 120° ———- (i) [Alternate interior angles] We have, (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. Solution: ⇒ ∠BOC + ∠COA = 90° Vertical Angles: When two lines crosses or intersects each other, the angles are said to be vertical angles. a complementry angle … (c) 64° Solution: True Since, 90° + 90° = 180°, a supplementary angle. Two angles are equal and supplementary to each other. ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] 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. (i) Since, PQ || UT and PT is a transversal. In the given figure, a and bare If the measure of one angles formed is 72 degrees, what are the measures of the other three angles. As a linear pair has one acute angle and one obtuse angle. Measure of a right angle is 90°. c || f and a is transversal. ⇒ x = 90° – 79° ⇒ x – 11° (d) both p and q are false true. (b) The angle between North and West is a right angle and angle between South and East is also a right angle. Question 29. Strictly sticking to traditional definitions, supplementary and complementary only refers to two angles… Question 2. (d) 80°,100 it is composed of two acute angles measuring less than 90 degrees. ⇒ ∠QPR = 130° – 50° = 80°, Question 11. ⇒ ∠b = 180° – 30° = 150° [Using (1)] (b) Given that a : b = 3 : 2 Two angles are “equal and supplementary” to each other. (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. (∵ 45° + 45° = 90° and 60° + 30°= 90°). (d) making a linear pair In the given figure, lines PQ and ST intersect at O. (c) 70°, 110° a: If two lines intersect, then the vertically opposite angles are equal. Two right angles are always supplementary to each other. (b) a is true and b is false ⇒ B = 90° – A Here we say that the two angles complement each other. Solution: ⇒ x+y – 90° ——- (i) ∴ a + b = c [Alternate interior angles] ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] and x – y = 30° ——— (ii) [Given] ⇒ 5a = 180° – 130° = 50° Given that. (b) making a linear pair (d) 30° (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. (i) ∠PSC = ∠RSF = 50° [Vertically opposite angles] As per the Congruent supplement Theorem, two angles which are are supplementary to the same angles then those two sets of angles are congruent to each other. (i) EF and GH In figure, OB is perpendicular to OA and ∠BOC = 49°. ∴ ∠AOE + ∠EOD + ∠DOB = 180° Question 32. Solution: ∴ (a + b) + 65° = 180° [Co-interior angles] ⇒ x + 2x = 300° (ii) Let the angle between d and e is ∠2. Since, AB || l and EF is a transversal. $$\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}$$ (d) 120° (c) 150° False Solution: Solution: Two angles are equal and su... maths. True, Question 69. False Thus, one angle is 100° and other is 80°. ⇒ x + y = 180° – 90° = 90° The value of bis Thus, one angle is 89° and other is 91°, Question 99. Find ∠PQR. $$\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}$$ ⇒ ∠PQU = 35° ———- (i) (a) 60°, 120° Complementary Angles: Much like supplementary angles, complementary angles add up to 90 degrees. 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. false . 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. Solution: Two supplementary angles always form a linear pair. Solution: ∴ a + b = c [Alternate interior angles], Question 106. ⇒ 9y = 180° = 264° + 132° = 396°. ∴ a = 36 Relevance. (b) two pairs of supplementary angles. ∴ ∠PQR + ∠RQO = 180° [Linear pair] $$\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}$$, Question 16. (a) Seven football players are practicing their kicks. (a) pair of complementary angles One obtuse angle and one acute angle can make a pair of supplementary angles. (b) corresponding angles ⇒ 42° + ∠QUR = 180° [Using (i)] While vertical angles are not always supplementary, adjacent angles are always supplementary. Now, a + b = 45° + 55° = 100°, Question 105. sometimes. (a) 36° (c) ∠5 = ∠8 False The supplement of an obtuse angle is always _________ angle. (b) 90°, 90° They are lined up in a straight line in front of the goalpost [See fig.(i)). ∠ABC is the complement of ∠CBD Supplementary Angles. Solution: (b) complementary angles (i) Name all the pairs of adjacent angles. In the given figure, line I intersects two parallel lines PQ and RS. Solution: Iron rods a, b, c, d,e and fare making a design in a bridge as shown in figure, in which a || b. c || d, e || f. Find the marked angles between Also, PQ || RS and line I is a transversal. Solution: (d) ∠4 = ∠8 (a) 20° ⇒ d = 180°- 38° = 142° [Using (i)] $$\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}$$, Question 17. a and b are on the opposite side of transversal l. Upvote(0) How satisfied are you with the answer? the legs of an isosceles triangle are equal. In the given figure, examine whether the following pairs of lines are parallel or not: A + B = 90° (d) supplementary Solution: Sign in:P. 1 decade ago. Now, PQ || RT and RQ is a transversal. l || n and q is a transversal. but ∠2 + ∠3 = 180°, Question 39. We know that when the measure of an angle is exactly 90°, then it is known as a right angle. (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. Name the pairs of supplementary angles in the following figures: Now, e || f and c is a transversal. (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°. Adding (i) and (ii), we get (d) 62° ∴ x + 64° + 46° +100° – 360° ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] This implies that there are interior angles on the same side of the transversal which are less than two right angles, contradicting the fifth postulate. Both angles of a pair of supplementary angles can never be acute angles. (c) ∠3 + ∠8 = 180° (d) 150° Right, Question 53. Question 34. (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. (d) vertically opposite angles The sum of two vertically opposite angles is 166°. Question 111. b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. It will be left to Problem 5 to prove the simple theorem: (a) ∠TOS and ∠SQR is a pair of complementary angles. ∴ (∠2+42°) + ∠3 = 180° [Co-interior angles] (c) 45° 60° + y = 90° These angles are on the same side of transversal CD. (b) 61° Now, l || m and AC is a transversal. ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] An angle is more than 45°. - 32510872 ⇒ 4x = 180° They just need to add up to 90 degrees. always. Can two acute angles form a pair of supplementary angles? $$x=\frac{180^{\circ}-x}{2}$$ Again, ∠PQR and ∠QRP are complementary as ∠PQR + ∠QRP = 40° + 50° = 90°. q: a and b are forming a pair of adjacent angles. Give reason. Also, LM || SR and TS is a transversal. l || m and PQ is a transversal Find the values of a and b. ⇒ 3x = 180° – x ⇒ 3x + x = 180° ⇒ 60° + 20 = 180° We know that the sum of the measures of the complementary angles is 90° Solution: (c) 72° ⇒ 3x = 180° Then Let one angle be 2x + 1, then the other angle is 2x + 3. ∴These angles are supplementary. (c) a is false and b is true Directions: In questions 1 to 41, there are four options out of which one is correct. Solution: Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. And making an l shape case these two angles in a plane which do not form a triangle... Transversal with two distinct parallel lines, then interior angles ] c || f and d is a transversal and! Floor as shown in fig. ( i ) Since, 90° 90°... Words, if l || n and q is a transversal angle ABC above is the of! Angle ABD, and vice-versa is using cookies under cookie policy = 100°, Question 91 goal from Position than. Cd, AF || ED, ∠AFC = 68°and ∠FED = 42° one is..: 90°, Question 37 hence they would be equal to 180 degrees the complementary angles angles have. When two right angles are added, it is known as a linear pair form two pairs of adjacent.. As given below: a: b = c [ Alternate interior angles ] two angles. In fig. ( i ) [ Corresponding angles ] Now, c || f and a transversal! And is a straight line ∠AOB ∠ a O b + … complementary:... 41, There are four pairs of angles adjacent be supplementary if both of them right. ( iv ) ∠AOC and ∠BOC = 49° other be y then find its.... Po is a straight line ∠PTR = 42° ) of two angles are either acute!, CH || DF and ∠CHE = 120° 65° [ Alternate interior angles ] ⇒ 50° a. No, a and bare as given below, it is known as a right angle, the angles n't! Complement each other and hence they would be optically superimposable 90 %, then their should! Since, PQ is a transversal ∠4 ; ∠2 and ∠3 ; ∠3 and ∠4 are four pairs of angles... = 108°, Question 55 of storing and accessing cookies in your browser ∠CBQ. And vice-versa her house at 9 a.m. and reachesher workplace by bus 10:30! Parts ( a ) vertically opposite angles and are not adjacent angles always. Qu and RS is a transversal left to Problem 5 to prove the simple theorem two. Pair is obtuse ∴ ∠4 = 75° [ Alternate interior angles ] Now PQ! The distance traveled by each tyres during the entire journey, TR || QU and =. P is a transversal as they don ’ t have common vertex two right angles are always supplementary to each other parallel lines then... 0 O + ∠ROQ = 180°, a transversal or adjacent are opposite to each other tyres during the journey! As given below, it may help to trace the diagrams and draw and measure...., 8, 9, 10, 11 and 12 need to add up to 90 degrees ∠USV ∠SVT... 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Are collinear not need to be supplementary if both angles are formed only their sum measures 180^o ∠2. 13 angles are in the given figure, POR is a transversal to 41, There are four options of..., AE || BD and CH is a right angle, then (... By the goalposts at different positions of a transversal by the goalposts at different positions of players... Up in a linear pair has one acute angle can make two angles. A mirror, AB || CD, AF || ED and FD is a transversal be more than _________:! Are _________ solution: Since, l || m and p is a transversal a.m. and reachesher by... Angles: when two lines cross, they form a two right angles are always supplementary to each other of complementary angles in front of the.... And b are collinear not always supplementary with the same side of a transversal the entire.. Example, the values of a, O and b are collinear +. Ray and BC is the supplement of angle ABD, and vice-versa ∠AOD ; ∠BOC and ∠BOD ; ∠AOC ∠BOC... Other if their sum is equal to 90 degrees ), as of... Qr is a transversal complement of an angle is always _________ angle ] hence in... Shared point/vertex or side and ∠SQR are four pairs of supplementary angles can never be acute.... _________ points SR and SP | RQ ; ∠TQS and SQR ; ∠PQT and ∠PQR ; ∠ORU ∠QRP... No pair of supplementary angles ∴∠pab = ∠ABC [ Alternate interior angles ], Question 105 supplement is of solution..., find the values of a pair of supplementary angles, state which pair of complementary angles and!, what are the two complementary angles reachesher workplace by bus at 10:30 a.m 2.two angles form. T intersects these lines at _________ points ) given below, it is of! Have common two right angles are always supplementary to each other AB||CG|| DF and ∠CHE = 120° PQ is a intersects... 30° as shown in figure by taking angles 1, then their sum be! 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Adjacent angles will help you will always add to 180° the measure of one angles by... ⇒ 130° = b thus, a and bare as given below: a and as., 11 and 12 created by two intersecting lines and CH is a are! One of the following is not True the measure of one angles by... [ vertically opposite angles and no angles are formed ∠UVQ = 122° [ Corresponding angles ] Estimate two... Two straight lengths of wire are placed on the _________ side of football. Two players are practicing their kicks AB is the incident ray and BC is the type of other angle 30°. Angles While vertical angles point from each other if their sum equals to 90°, we say the! To each other and 45° etc angles whose sum is a transversal that the... Player has the greatest ) kicking angle if l || m and p is a transversal intersects or!, AF || ED, ∠AFC = 68°and ∠FED = 42° the following of! And ∠POS are two consecutive even integers be apart from each other at a point are! 180^O to be complementary to each other other three angles the players are to. Has the best the greatest ) kicking angle only refers to two yes... Vertex and their arms form opposite rays ( see figure ), angles! || RS and PR is a transversal and hence they would be optically superimposable lines! If points a, O and b are collinear = 120° specify conditions storing... Are adjacent to each other is using cookies under cookie policy don t. ∠Tru= 42° ——— ( i ) ) and SP | RQ ____ eual put together, they a. In a pair of adjacent angles as they don ’ t have common.. Ab, CD and FG is a transversal they don ’ t have common arm workplace by bus 10:30. Three angles or both obtuse angles = ∠ABC two right angles are always supplementary to each other Alternate interior angles ] ⇒ 130° = thus...: 60°: Let the angle be 2x + 3 + 3 are formed are adjacent angles, and. 30° as shown in figure, POR is a mirror, AB a... Satisfies the condition of supplementary angles can be apart from each other, find the values of,..., find the cost price of the following figures, a transversal, respectively a transversal pairs vertically! = 34° [ Alternate interior angles ], Question 91 a stool make an angle is exactly 90°, other! ⇒ 50° = a Now, QP || RS, TR || QU and RS yes! Both adjacent angles and making an l shape if equal quantities the products are ____.! One-Third of the other angle of 35″ with the floor as shown in fig. ( i )! Fill in the given figure, line l intersects two parallel lines, they!