# Isosceles Meld

Weekly Problem 9 - 2012

What is the angle QPT in this diagram?

What is the angle QPT in this diagram?

## Problem

Image

In the diagram PQ = PR = RS.

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

Triangle PQR is isosceles therefore angle PQR = angle PRQ = 72 degrees.

Triangle PSR is also isosceles therefore angle RPS = angle RSP = 36 degrees.

Therefore x = (180-36-36) degrees = 108 degrees.