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Extended Parallelogram

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2


Opposite angles of a parallelogram are equal, so ∠QPS = 50°. Therefore, ∠QPT = 112° and, as triangle QPT is isosceles, ∠PQT = (180°-112°)/2=34°. As PQRS is a parallelogram, ∠PQR = 180° - 50° = 130°.

So ∠TQR = 130° - 34° = 96°.


This problem is taken from the UKMT Mathematical Challenges.