Question

In fig 3.32 . If $AB||CD,\angle APQ={50}^{\circ }$ and $\angle PRD={127}^{\circ }$ , find x and y

Answer 1

If $AB||CD$ and $\angle APQ={50}^{\circ }$ and $\angle PRD={127}^{\circ }$ , then $\angle x=?\angle y=?$
$\therefore \angle APQ=\angle PQR=x$
$50=\angle PQR=x$
$\therefore x={50}^{\circ }$
similarly , $AB||CDPR$ straight line intersects these at P and R
$\therefore \angle APR=\angle PRD$
$\angle APQ+\angle QPR=\angle PRD$
$50+\angle QRP=127$
$\angle QPR=127-50$
$\therefore \angle QPR={77}^{\circ }$
$\angle QPR=y={77}^{\circ }$
$\therefore x={50}^{\circ }$
$y={77}^{\circ }$