WAEC Mathematics 2015 Objective — Question 19

Question 19 of 50 from the West African Examinations Council (WAEC) Mathematics 2015 Objective paper, with the correct answer and a full explanation.

In the diagram above, O is the centre of the circle, line RT is a diameter, ∠PQT = 33° and ∠TOS = 76°. Calculate the value of angle PTR.

• A. 73°
• B. 67°
• C. 57°Correct
• D. 37°

Explanation

Since RT is a diameter, ∠RPT=90° (angle in semicircle). ∠PQT=∠PRT=33° (angles in the same segment). In triangle PRT: ∠PTR = 180−(90+33) = 57°.

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