In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
30°, 250°
In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
126°
In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
Sum of all the angles at a point = 360°
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).
∠QOS = ∠SOR + ∠ROQ and ∠POS = ∠POR − ∠SOR.
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.
122°, 302°
In Fig. 6.23, if \(AB \parallel CD\), \(CD \parallel EF\) and \(y : z = 3 : 7\), find \(x\).
\(126^\circ\)
In Fig. 6.24, if \(AB \parallel CD\), \(EF \perp CD\) and \(\angle GED = 126^\circ\), find \(\angle AGE\), \(\angle GEF\) and \(\angle FGE\).
\(126^\circ\), \(36^\circ\), \(54^\circ\)
In Fig. 6.25, if \(PQ \parallel ST\), \(\angle PQR = 110^\circ\) and \(\angle RST = 130^\circ\), find \(\angle QRS\).
\(60^\circ\)
In Fig. 6.26, if \(AB \parallel CD\), \(\angle APQ = 50^\circ\) and \(\angle PRD = 127^\circ\), find \(x\) and \(y\).
\(x = 50^\circ\), \(y = 77^\circ\)
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 \(AB \parallel CD\).
Angle of incidence = Angle of reflection. At point \(B\), draw \(BE \perp PQ\) and at point \(C\), draw \(CF \perp RS\).