Question

Find $\angle APB$, if $AE||BR$.

Answer 1

given $AE\parallel BR$

Now AB acts as transversal.

$\angle A+\angle B={180}^{\circ }$ (interior angles of same side of transversal are supplementary )

$\therefore 2x+2y={180}^{\circ }$

$2(x+y)={180}^{\circ }$

$x+y={90}^{\circ }$

Now in $\Delta APB$

$\angle PAB+\angle PBA+\angle APB={180}^{\circ }$

$X+Y+\angle APB={180}^{\circ }$

But $x+y={90}^{\circ }$

$\therefore \angle APB={180}^{\circ }-(x+y)$

$\angle APB={180}^{\circ }-{90}^{\circ }$

$\angle APB={90}^{\circ }$