Question

Find the angles $x$ and $y$ in the adjoining figure.

Answer 1

From the given fig.

In $\Delta PLQ$

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

$\Rightarrow \angle PQL+\angle PLQ+\angle LPQ={180}^{\circ }$

$\Rightarrow x+90+34=180$

$\Rightarrow x+124=180$

$\Rightarrow x=180-124$

$\Rightarrow x={56}^{\circ }$

From the angle property

$\angle x=\angle y$

$\Rightarrow \angle x=\angle y={56}^{\circ }$