What is the value of $\angle x + \angle y$ in the following diagram?

Question

$\angle p=30^\circ$, $\angle q=45^\circ$, $\angle r=50^\circ$, $\angle$ $s=25^\circ$. $\angle x + \angle y = ?$

Source: Bangladesh Math Olympiad 2016 junior Category

I could not find any ways to get $\angle x + \angle y$.

Answer 1

This is an irregular hexagon so the sum of the interior angles is $720^\circ.$

$\angle p+\angle q +\angle r + \angle s + (360^\circ-\angle x) + (360^\circ - \angle y)= 720^\circ$
$30^\circ+45^\circ+50^\circ+25^\circ+360^\circ-\angle x+360^\circ-\angle y=720^\circ$
$150^\circ=\angle x+\angle y$

All the best for the olympiad.

Answer 2

Hint: The sum of the angles in an $n$-gon is $(n-2)\cdot 180^\circ$