In Fig. 6.25, if $PQ \parallel ST$, $\angle PQR = 110^{\circ}$ and $\angle RST = 130^{\circ}$, find $\angle QRS$. [Hint : Draw a line parallel to ST through point R

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

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

In Fig. 6.27, 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 $AB \parallel CD$

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