enter image description here

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

Source: Bangladesh Math Olympiad 2016 junior Category

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


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.

  • $\begingroup$ 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

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

  • $\begingroup$ did you mean that this diagram is a hexagon? $\endgroup$ – Shromi Jan 26 at 17:04
  • 1
    $\begingroup$ 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
  • 1
    $\begingroup$ If it's made up of straight line segments like that, yes. $\endgroup$ – Michael Biro Jan 26 at 17:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.