NCERT Solutions
Class 9 - Mathematics

Chapter 6: LINES AND ANGLES

In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.

In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.

In Fig. 6.17, 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.

In Fig. 6.23, if \(AB \parallel CD\), \(CD \parallel EF\) and \(y : z = 3 : 7\), find \(x\).

In Fig. 6.24, if \(AB \parallel CD\), \(EF \perp CD\) and \(\angle GED = 126^\circ\), find \(\angle AGE\), \(\angle GEF\) and \(\angle FGE\).

In Fig. 6.25, if \(PQ \parallel ST\), \(\angle PQR = 110^\circ\) and \(\angle RST = 130^\circ\), find \(\angle QRS\).

In Fig. 6.26, if \(AB \parallel CD\), \(\angle APQ = 50^\circ\) and \(\angle PRD = 127^\circ\), find \(x\) and \(y\).

In Fig. 6.27, PQ and RS are two mirrors placed parallel to each other. A ray \(AB\) strikes mirror PQ at \(B\), reflects along \(BC\), then hits mirror RS at \(C\) and reflects back along \(CD\). Prove that \(AB \parallel CD\).