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

Source: Bangladesh Math Olympiad 2016 junior Category

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

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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.

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  • $\begingroup$ Thanks for the answer and early blessings! $\endgroup$ – Shromi Jan 26 at 17:07
  • $\begingroup$ Me too. Brother in which class do you study? $\endgroup$ – Shromi Jan 26 at 17:10
  • $\begingroup$ Don't worry it will be published in Prothom Alo or in the Facebook groups $\endgroup$ – Shromi Jan 26 at 17:44
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Hint: The sum of the angles in an $n$-gon is $(n-2)\cdot 180^\circ$

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

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