Isosceles Meld
Age
11 to 14
Challenge level
Weekly Problem 9 - 2012
What is the angle QPT in this diagram?
Problem
Image
In the diagram PQ = PR = RS.
If angle QPR is 36 degrees, find the size of angle QPT?
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.