Isosceles Meld
Weekly Problem 9 - 2012
What is the angle QPT in this diagram?
What is the angle QPT in this diagram?
Age
11 to 14
Challenge level
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.