[Math] Getting the angles of a triangle

geometrytriangles

I am having trouble with the following question

In the following figure if PQ=QS and QR=RS and angle PRS is 100 degrees what is the measure of angle QPS (Ans = 20)

enter image description here

Now here is how far i got:
Since QR=RS its angles would be same and we know that PRS is 100 so we get

2a + 100 = 180 so a = 40 so RQS is 40 and QSR is 40 . Am I doing this correct ? How will i get PSQ or QPS ? (I need to do this without Trign. ratios)

Best Answer

So far so good! Now noticing that $\angle QRS + \angle QPS + \angle QSP + \angle QSR = 180$, then just like you did before, since $\triangle PQS$ is isosceles, $\angle QPS = \angle QSP$. So plugging in,

$100 + 2 \angle QPS + 40 = 180$ and $\angle QPS = 20$!

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