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NCERT solutions Mathematics Textbook for Class 9 chapter 6 Lines and Angles

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Chapter 6 - Lines and Angles

Pages 96 - 97

In the given figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Q 1 | Page 96 | view solution

In the given figure, lines XY and MN intersect at O. If ∠POY = 90° and a:b = 2 : 3, find c.

Q 2 | Page 97 | view solution

In the given figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Q 3 | Page 97 | view solution

In the given figure, if x + y = w + z, then prove that AOB is a line.

Q 4 | Page 97 | view solution

In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = 1/2(∠QOS - ∠POS).

Q 5 | Page 97 | view solution

It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Q 6 | Page 97 | view solution

Page 105

In the given figure, find the values of x and y and then show that AB || CD.

Q 1 | Page 105 | view solution

In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.

Q 2 | Page 105 | view solution

In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126º, find ∠AGE, ∠GEF and ∠FGE.

Q 3 | Page 105 | view solution

In the given figure, if PQ || ST, ∠PQR = 110º and ∠RST = 130º, find ∠QRS.

[Hint: Draw a line parallel to ST through point R.]

Q 4 | Page 105 | view solution

In the given figure, if AB || CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.

Q 5 | Page 105 | view solution

In the given figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.

Q 6 | Page 105 | view solution

Pages 107 - 108

In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

Q 1 | Page 107 | view solution

In the given figure, ∠X = 62º, ∠XYZ = 54º. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ΔXYZ, find ∠OZY and ∠YOZ.

Q 2 | Page 107 | view solution

In the given figure, if AB || DE, ∠BAC = 35º and ∠CDE = 53º, find ∠DCE.

Q 3 | Page 107 | view solution

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

Q 4 | Page 107 | view solution

In the given figure, if PQ ⊥ PS, PQ || SR, ∠SQR = 28º and ∠QRT = 65º, then find the values of x and y.

Q 5 | Page 108 | view solution

In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR = 1/2∠QPR.

Q 6 | Page 108 | view solution

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