Mathematics
Grey Kangaroo
2023
13

13

In the diagram shown, sides PQ and PR are equal. Also ∠QPR = 40◦ and ∠TQP = ∠SRQ. What is the size of ∠TUR?

A. 55◦ B. 60◦ C. 65◦ D. 70◦ E. 75◦

Answer

D.

SOLUTIOn

Let ∠SRQ be x ◦ . Since sides PR and PQ are equal, triangle PQR is isosceles and hence ∠PRQ = ∠PQR = (180◦ − 40◦ )/2 = 70◦ . Therefore, since we are given that ∠TQP = ∠SRQ, we have ∠UQR is 70◦ − x ◦ . Hence, since the exterior angle of a triangle is equal to the sum of the interior opposite angles, ∠TUR is 70◦ − x ◦ + x ◦ = 70◦ .

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