Question

Question 5
In the given figure, if $AB||CD,\angle APQ={50}^{\circ }and\angle PRD={127}^{\circ },$ find x and y.

Answer 1

$\angle APR=\angle PRD$ [Alternate interior angles]
${50}^{\circ }+y={127}^{\circ }$
$y={127}^{\circ }-{50}^{\circ }$
$y={77}^{\circ }$
Also, $\angle APQ=\angle PQR$ [Alternate interior angles]
${50}^{\circ }=x$
$\therefore x={50}^{\circ }andy={77}^{\circ }$