EXERCISE

In the given figure, find the values of $x$ and $y$ and then show that $AB\parallel CD.$

In the given figure, if $AB\parallel CD, CD\parallel EF$ and $y:z=3:7,$ find $x.$

In the given figure, if $AB\parallel CD, EF\perp CD$ and $\mathrm{\angle }GED=126°,$ find $\mathrm{\angle }AGE, \mathrm{\angle }GEF$ and $\mathrm{\angle }FGE.$

In the given figure, if $PQ\parallel ST, \mathrm{\angle }PQR=110°$ and $\mathrm{\angle }RST=130°,$ find $\mathrm{\angle }QRS.$

In the given figure, if $AB\parallel CD, \mathrm{\angle }APQ=50°$ and $\mathrm{\angle }PRD=127°,$ 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 $AB\parallel CD.$