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 \(CF \perp RS\).