Extended parallelogram
Weekly Problem 11 - 2014
The diagram shows a parallelogram and an isosceles triangle. What is the size of angle TQR?
Age
11 to 14
Challenge level
Problem
Image
In the diagram, PQRS is a parallelogram; ∠QRS = 50 °; ∠SPT = 62 ° and PQ = PT. What is the size of ∠TQR?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
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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 °.