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JAMB Mathematics 2012 Question 27

Question 27

Circle Theorems

In the diagram above, PQR is a circle centre O. If ∠QPR is x°, find ∠QRP.

Diagram for this question
  1. A.x°
  2. B.(90 − x)°
  3. C.(90 + x)°
  4. D.(180 − x)°
Show the answer and explanation

Answer: B ((90 − x)°)

Explanation

PR passes through O, so it is a diameter and ∠PQR = 90°. The angles of triangle PQR add to 180°, so ∠QRP = 90° − x.