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UI Post-UTME Mathematics 2024 (Model questions) Question 22

Question 22

Triangles and Quadrilaterals

In the figure below |PQ| = |PR| = |PS| and SR̂T = 68°, find QP̂S

Diagram for this question
  1. A.68°
  2. B.112°
  3. C.136°
  4. D.56°
Show the answer and explanation

Answer: C (136°)

Explanation

Triangles PQR and PRS are isosceles, so ∠PRQ = ∠PQR and ∠PRS = ∠PSR. On the straight line at R, ∠PRQ + ∠PRS = 180° − 68° = 112°. Then ∠QPS = (180° − 2∠PRQ) + (180° − 2∠PRS) = 360° − 224° = 136°.