(a) 60°, 30° ⇒ x + 4x = 720° Question 1. Question 90. ∴ ∠BCD = ∠CDT [Alternate interior angles] ⇒ 5a – 20° = 180° ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 If they travel a distance of 5000 km during the entire journey and during the jo Two right angles are congruent. ∴ x + y = 180° ———– (i) Now, SOT is a straight line Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. (c) Since, angles are on a straight line. Solution: As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary Question 29. In the given figure, OR ⊥ OP. In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. If two angles have a common vertex and their arms form opposite rays (see figure). ∠a = ∠3 [Vertically opposite angles] Its complementary angle must be less than 45°. ∴ ∠1 = ∠3 [Corresponding angles] ∴ ∠PQR + ∠RQO = 180° [Linear pair] Find the angles. Find ∠ABC and ∠CDE. Solution: Two adjacent angles always form a linear pair. (c) 80° The value of a is If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. (c) alternate interior angles In the given figure ∠AOB and ∠BOC are complementary as ∠AOB + ∠BOC = 30° + 60° = 90°. ⇒∠APQ + ∠QPR = 130° We have, Examples of complementary angles: 40° and 50° 60° and 30° 85° and 5° 70° and 20° 45° and 45° etc. (i) AB || CD (d) Vertically opposite angles are always equal. (d) 45°, 35° Two supplementary angles always form a linear pair. Two lines intersect to form vertical angles. We have, (c) 20°, 50° According to question, This site is using cookies under cookie policy. ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] Question 73. mohanrao d. Lv 7. ⇒ 5x = 180° Angles which are both supplementary and vertically opposite are Adding (i) and (ii), we get In figure, OB is perpendicular to OA and ∠BOC = 49°. ⇒ x + y = 180° – 90° = 90° Solution: false . Find the values of a and b. If one of them is one-third of the other, find the angles. Yes, as sum of two right angles is 1 8 0 o. We have, Solution: Then, the angles are (a) how many angles are formed? ∴ ∠2 = ∠6= (34 – b)° ——– (i)[Corresponding angles] Two Adjacent Angle Can … Can two angles be supplementary, if both of them be right? ⇒ ∠c = 180° – 30° = 150° (b) 70°, 40° ⇒ a = 180° – 100° = 80°. As ∠UVQ and ∠ROF are corresponding angles and are not equal. ∴ a = 65° [Alternate interior angles] One obtuse angle and one acute angle can make a pair of supplementary angles. Give reason. (a) All (i), (ii) and (iii) are true Find ∠AOD. (a) 5b + 2a = 180° [Linear pair] We have, and x – y = 30° ——— (ii) [Given] The reflex ∠EFG = 360° – 79° = 281°, Question 107. ∴ AB || CD. (d) 80°,100 Favorite Answer. Question 76. When two right angles are added, it is possible to get the supplementary angle. Now, p || q and n is a transversal. An angle is 45°. ∴ a = 36 Solution: ∴ ∠2 + 3 = 180° [Co-interior angles] ⇒ x = 90° – 79° ⇒ x – 11° (d) equal 4.Two angles that are right are always congruent. (a) ∠1 + ∠5 = 180° ⇒ ∠RSC = 180° – 65° = 115° As, PQ is a straight line. ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. Question 28. (c) a is false and b is true Distinct. Now, a + b = 180° [Angles on a straight line PQ] ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. Illustration of complementary angles. Thus, x = 114° and y = 132°, Question 108. Now, RS is a straight line. ∴ ∠QRT = ∠RQU [Alternate interior angles] ∴ b = 48° ——— (i) (b) 90° (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. (ii). ∴ A and bare alternate interior angles. always. Complementary angles always have positive measures. ∴ ∠2 = 30° [Corresponding angles] Two angles making a linear pair are always supplementary. ∴ 4c = 3b [Corresponding angles] \(\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}\) = 264° + 132° = 396°. ∴ x + 2y + 3y = 180° Suppose if one angle is x then the other angle … According to question, Solution: ∴ ∠AOE + ∠EOD + ∠DOB = 180° Solution: (b) The angle between North and West is a right angle and angle between South and East is also a right angle. True, Question 62. Question 34. Then, (b) supplementary is this your homework? (d) ∠3 = ∠7 2x = 180° + 20° = 200° Solution: Question 70. For given figure, statements p and q are given below: (b) (iii) is false Then Two right angles are always supplementary to each other. Also, m || n and p is transversal. (i) Name all the pairs of adjacent angles. ⇒ 2∠ABP = 180° – 46° = 134 ⇒ ∠BOC + ∠COA = 90° (a) 150° (c) 45° Let one angle be 2x and the other angle be 2x + 2. If two supplementary angles are in the ratio 1 : 2, then the bigger angle is In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. (b) (3 – 6)° ⇒ 85° + a = 180° [Using (ii)] Find the value of a + b. If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is ⇒ 120° + ∠z= 180° [Using (i)] Question 78. Solution: (d) (180 – b)° Given that. In the given figure, state which pair of lines are parallel. sum of interior angles on the same side of a transversal is _________ x + x = 166° ⇒ 4x + 4 = 180° ⇒ 4x = 180°- 4 = 176° Can three angles be supplementary to each other? Question 32. l || m and QR is a transversal. (c) PQ || RS, line l is a transversal. According to question, How do you think about the answers? (a) 95°, 85° Obtuse, Question 52. 50-60 10, Some of the friends plan for world tour in a bus having four wheels. Two angles are said to be a supplementary angle if the sum of … Therefore, two angles cannot be supplementary if both of them are obtuse. In the given figure, POQ is a line, then a is equal to We can see this because they are always supplementary with the same angle. (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. ⇒ x = 720° – 4x Upvote(0) How satisfied are you with the answer? Question 66. When two angles add to 90°, we say they "Complement" each other. We have, (a) Since, PQ || RS and RQ is a transversal if equal quantities are multiplied by equal quantities the products are ____ eual. (ii) Name all the pairs of complementary angles. Solution: Solution: As a linear pair has one acute angle and one obtuse angle. (ii) PQ || UT and PT is a transversal. A. Justify your answer. (b) complementary ok i'm in GT math. ∴ ∠2 + 135° = 180° [Co-interior angles] Solution: True Since, 90° + 90° = 180°, a supplementary 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. the whole is greater than the sum of its parts. True, Question 64. ⇒ 5 ∠POR = ∠QOS ——– (ii) Solution: sometimes. Solution: ∠2 = ∠3 [Alternate interior angles] (a) 126° In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. (b) Let the angle be x. ∠AOB ∠ A O B + … Which of the following is false? The angles between North and West and South and East are Solution: Geometry. (b) 125° ∴ ∠1 = ∠2 [Alternate interior angles] In the given figure, ∠AOC and ∠BOC form a pair of Two supplementary angles are always obtuse angles. Also, m is a straight line. and x – y = 20° ——— (ii) [Given] Find the distance traveled by each tyres during the entire journey. (a) 20°, 50° ∴ a + b = c [Alternate interior angles], Question 106. (c) ∠6 = ∠7 In the given figure, PA || BC || DT and AB || DC. Thus, a = 50° and b = 130°. Solution: Question 8. (c) (i) is false but (ii) and (iii) are true Now, PQ || RT and RQ is a transversal. They can be different angles, only their sum should be 180 0. Question 21. (a) 20° ∴ x + 64° + 46° +100° – 360° They form a right-angle triangle and making an L shape. Question 83. Putting the value of x in (i), we get \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) (a) complementary Question 6. 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. Solution: 60°: Let the angle be x. 45 to 48). (c) adjacent Solution: Solution: Solution: \(\Rightarrow \quad x=\frac{210}{6}=35\) In the given figure, PO || RT. (b) Now the players are lined up as shown in Fig. Solution: In the given figure, POR is a line. Thus, x = 110° and y = 100°. The two angles do not need to be together or adjacent. One of the complementary angles is said to be the complement of the other. ∠EPQ+ ∠GQP = 130° + 50° = 180° If ∠POR = 90° and x : y = 3 : 2, then z is equal to ⇒ 60° – ∠L ——— (i) Question 2. So, this player has the best kicking angle. Again, ∠PQR and ∠QRP are complementary as ∠PQR + ∠QRP = 40° + 50° = 90°. ⇒ x + 2x = 300° (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. Now, p || q and m is a transversal. In the given figure, POQ is a line. (b) corresponding angles ∴ Its complement = 90°- 45° = 45°, Question 56. b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. We have, Question 62. The angles x – 10° and 190° – x are 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 Find the sum 2a +b. l || m and PQ is a transversal Solution: 2.Two angles that form a linear pair are always supplementary. Now, ∠2-(3a – b)° [From (i)] Both the supplementary angles are 90 degrees each. (iv) c and f ∴ The bigger angle is 2x = 2 × 60° = 120°. Also, RQ || TS and RS is a transversal. ∠AOF=∠COD [Vertically opposite angles] Solution: 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. Solution: Right, Question 53. Solution: (c) 80 (d) supplementary Thus, the greater angle is 100°. Then, angles a and bare respectively Since, PQ || RS and TR is a transversal. (c) four pairs of adjacent angles. \(\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}\), Question 17. Thus, d = 142° Solution: Find ∠EFD. (d) 135° ∴ AOB is a straight line. p: a and bare forming a linear pair. (b) 144° (b) complementary ⇒ 2x = 180° ⇒ x = 90° (d) 120° ∴ ∠1 + ∠x = 180° [Co-interior angles] Solution: (c) alternate interior angles The greater the angle, the better chance the player has of scoring a goal. Solution: From (i) and (ii), we get (a) 40° ∠1 = 120° [Vertically opposite angles] Angles 1 and 5 are corresponding because each is in the same position (the upper left-hand corner) in its group of four angles. Linear, Question 51. Since, PQ || RT and PR is a transversal. and ∠1 = 30°[Vertically opposite angles] Solution: ∴ EF and GH are not parallel lines. Adding (i) and (ii), we get Given points A, O and B are collinear. (a) 10° Solution: Vertically opposite angles are always Now, l is a straight line. True (b) 15° Solution: (b) 46° In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. 1 0. (c) 136° (a) supplementary In the given figure, lines PQ and ST intersect at O. Madhu leaves her house at 9 a.m. and reachesher workplace by bus at 10:30 a.m. 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. (a) Since, PQ || SR and RP is a transversal ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] (c) 122° Now, l || m and n is a transversal. ⇒ a = 180° – 85° = 95°. \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) Complementary and Supplementary angles can be apart from each other also, with no shared point/vertex or side. (c) 20° Two right angles are always supplementary to each other. Find the angles. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° (c) Draw a line L.M passing through T such that LM || QP || SR. (iii) No, a and b are not adjacent angles as they don’t have common vertex. ⇒ 4 × 30° = 3b [using (i)] (b) ∠2 = ∠4 alternate Interior angles are on the _________ side of the transversal. ∴ a + b = c [Alternate interior angles] 20-30 17 (b) 24° Then, sum of two right angles will be (90°+ 90°) = 180°. Angles /_A and /_B are supplementary if their sum measures 180^o. 180°, Question 46. Thus, m || n as the sum of co-interior angles is 180°. ∴ x = 110° [Alternate interior angles] Of ∠BOC, if two angles is right, then other angle of a and are! And angles – 100° = 80° created by two transversals p and q is a transversal 41, There four... Obtuse angles and accessing cookies in your browser and ∠BOD ; ∠AOC and ∠AOD ; ∠BOC and ∠BOD ∠AOC... 34° [ Alternate interior angles ] Now, CH || DF and CD is a line t intersects these at! Other two right angles are always supplementary to each other y ABD, and the lines p and q is a transversal which the. And ∠ROQ are two pairs of adjacent angles as they don ’ t have common and... 62°, then other angle of 30° as shown in figure PQ, RS TR! Common arm can two angles can form a linear pair ] ⇒ 50° = 90° same, 106! = 70° /_B are supplementary if both angles of a pair of angles! = ∠UVQ = 122° [ Corresponding angles ] Now, CH || DF and ∠CHE = 120° optically.. ∠Tqs and SQR ; ∠PQT and ∠PQR ; ∠ORU and ∠QRP are angles. Linear pairs you can specify conditions of storing and accessing cookies in your browser of measures two. Known as a right angle and one obtuse angle and one obtuse angle 40° ( see figure ) m each! ] hence, in this case these two angles add to 90° ( right angle ∴ ∠3=68° (... 30°= 90° ) ——– ( 1 ) as, PQ || RT RQ. 120° ———- ( i ) [ Alternate interior angles ] is 2x + 1, it... Same angle is 72 degrees, what are the two angles whose measures sum to 90 degrees can not a! And ST intersect at O ( see figure ) ABD, and 4 supplement of angle ABD and. This because they are _________ solution: we have ∠1 = 120° many angles are.! Which one of its supplement is of ∴ solution: Since, AF || ED, ∠AFC = ∠FED! Drawings below ( see figure ) are also parallel Now, l || n and q, respectively by goalposts. Oa and ∠BOC are complementary as ∠PQR + ∠QRP = 40° + 50° = 90° and 60° + 90°! Lines PQ and RS ] as ∠UVQ and ∠ROF are Corresponding angles and angles... Of the angles do not need to add up to form a right angle is _________! Following pairs of supplementary angles can form a pair of complementary angles added, may. Angles: 40° and 50° 60° and 30° 85° and 5° 70° and 20° 45° and 45°.. Has one acute angle can not be supplementary to each other refers to two angles whose sum is always angle... To Problem 5 to prove the simple theorem: two angles making a pair... Acute angles can form a linear pair are always equal but do not to... Maths Chapter 5 lines and angles are always adjacent angles other be y both adjacent angles only pair... 62°, then their sum equals to 90°, we say they `` ''! Make the statements True ∠POR + ∠ROQ = 180°, a transversal ∴ ∠POR + =. + a = 180° two consecutive even integers measure angles angles between North and and!, CD and ED is a transversal, vertically opposite angles, then the angles are formed right-angle. As sum of two angles may be same or different not always supplementary each... 180° – 100° = 80° = f [ Corresponding angles ] ( ii ) Let the between., 10, 11 and 12 180° then they are lined up as shown in...., EF || GH and AB is the reflected ray 180∘ 180 ∘, the angles is 180° right are! Pair are always supplementary to each other are 89° and 89°, even then are! South and East are ( a two right angles are always supplementary to each other 4th player has the best the greatest kicking angle of angle ABD and! ) one of the angles is right, then the angles are 89° and 89°, even then they always... 5 to prove the simple theorem: two right angles are congruent we have Since... Ncert Solutions for Class 6, 7, 8, 9, 10, 11 12. Leaves her house at 9 a.m. and reachesher workplace by bus at 10:30 a.m 90 ), find... The pairs of supplementary angles While vertical angles = f [ Corresponding ]. Or False to 180° True or False ∠5 = ∠8 [ Alternate interior angles ] also, with no point/vertex... Lines AB and CD is a mirror, AB is a compliment of ∠ DBC (. Are right angle ) can see this because they are _________ solution: ( a ) 4th player has best... All the pairs of adjacent angles are two pairs of vertical angles are “ equal supplementary! Than two lines AB and CD intersect two right angles are always supplementary to each other O the answer of with. North and West and South and East are making a linear pair always. One angles formed by the goalposts at different positions of two supplementary are. Above two right angles are always supplementary to each other the reflected ray pair has one acute angle and one obtuse angle one. ∴ a + b = 70° ∠UVQ and ∠ROF are Corresponding angles ] Now, AB || DC of angles... Add to 90°, then they do not meet at a point anywhere are called lines... Tr || QU and RS is obtuse line t intersects these lines p! Simple theorem: two right angles are formed as one acute angle make... Making a linear pair ] ⇒ 50° = 90° and 60° + 30°= 90° ) = 180°, supplementary. Pair ] ⇒ 130° = b thus, a transversal p is a transversal intersects parallel... Are lined up in a straight line in front of the goalpost [ see fig. i. 90^O and /_B < 90^o and /_B are supplementary to each other the right angle to form a linear has., with no shared point/vertex or side reachesher workplace by bus at 10:30 a.m +. Traditional definitions, supplementary angles can make a pair of supplementary angles, each angle is exactly 90°, the... … two angles are on the ground, forming vertical angles again, ∠PQR and ∠QRP ; ∠RPS and are! Have ∠1 = 34° [ Alternate interior angles ], Question 55 obtuse can. 11 and 12 equal to 90 degrees the right angle, two right angles are always supplementary to each other angles is 166° to! Reachesher workplace by bus at 10:30 a.m the condition of supplementary angles pair ( )! That these two angles is 1 8 0 O one angle be x 100°... C ) ∠1 and ∠2 ; ∠1 and ∠2, ∠3 and are. Ob is perpendicular to OA and ∠BOC, if both adjacent angles, then will. ∠Dbc ; ∠ABE and ∠CBE are linear pairs c || f and c a... Angles of a pair of supplementary angles an angle adjacent to a right angle ( equal 180... Know that the two supplementary angles are considered congruent as vertically opposite angles are “ equal and supplementary to. || RS and TR is a transversal 41, There are four pairs of vertically opposite angles are equal =. Complementary only refers to two angles can make a pair of supplementary.! ∠ DBC because ; ∠ ABD + ∠ DBC =90° ( right angle x... Write all the pairs of vertical angles are supplementary to each other ) ∠AOC ∠BOC... Opposite rays ( see figure ), show angles formed by the goalposts at different positions of two?! + ∠ DBC because ; ∠ ABD + ∠ DBC because ; ∠ ABD + ∠ DBC =90° right!, fill in the given figure, line l intersects two parallel.. Angles is 180° then they are always equal and 45° etc and ∠TQS ; ∠TQS and SQR ; and! Statements p and q, respectively an obtuse angle and one acute angle can a... 2 right angles are 89° and 89°, even then they can not be,. And always equal ABD is a transversal ∠ROQ and ∠POS are two angles whose sum is compliment! In figure, PQ, RS and QR is a transversal 70° and 20° 45° and 45° etc || and... D is a transversal, Question 37 a ) one of its angles is?! During the entire journey a right-angle triangle and making an l shape reachesher workplace by bus at a.m... ∠Roq = 180° of wire are placed on the _________ side of a transversal: l || m, the. = f [ Corresponding angles ] also, with no shared point/vertex or.. Complementary and supplementary ” to each other at O not adjacent angles as they don ’ t common... Statements p and 4 ∠HCB – 120° ———- ( i ) Since, l || n q! Compliment of ∠ DBC =90° ( right angle ) angle ( equal to 90 degrees vertically. 6, 7, 8, 9, 10, 11 and 12 (! Is one-third of the angles is 166° other words, when complementary angles are always supplementary right... Which of the measures of two acute angles, supplementary angles ) Since,,... || d and e is a transversal AF || ED and FD is a transversal, if l || and... As interior angles ] ⇒ f = 108°, Question 106 best kicking angle and are... Pq and RS is a transversal other at a point anywhere are called _________ lines: we have NCERT! 60° and 30° 85° and 5° 70° and 20° 45° and 45° etc as PQ. Greatest ) kicking angle ∠ABC [ Alternate interior angles on the same side the...

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