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

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

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

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.

• Thanks for the answer and early blessings! – Shromi Jan 26 at 17:07
• Me too. Brother in which class do you study? – Shromi Jan 26 at 17:10
• Don't worry it will be published in Prothom Alo or in the Facebook groups – Shromi Jan 26 at 17:44

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

• did you mean that this diagram is a hexagon? – Shromi Jan 26 at 17:04
• Yes, that's right. – Michael Biro Jan 26 at 17:04
• Thanks I got the answer. But is all these type of diagrams are a polygon? – Shromi Jan 26 at 17:06
• If it's made up of straight line segments like that, yes. – Michael Biro Jan 26 at 17:14