#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Coordinate Geometry

Chapter 4 - Linear Equations in two Variables

Chapter 5 - Introduction to Euclid's Geometry

Chapter 6 - Lines and Angles

Chapter 7 - Triangles

Chapter 8 - Quadrilaterals

Chapter 9 - Areas of Parallelograms and Triangles

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Heron's Formula

Chapter 13 - Surface Area and Volumes

Chapter 14 - Statistics

Chapter 15 - Probability

## 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.

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

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

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

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).

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.

#### Page 105

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

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

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

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

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

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

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.

#### 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.

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.

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

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

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

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.