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WAEC Mathematics 2013 Question 43

Question 43

Angles and Polygons

In the diagram, ST//PQ, reflex angle SRQ = 198° and ∠RQP = 72°. Find the value of y.

Diagram for this question
  1. A.18°
  2. B.54°
  3. C.92°
  4. D.108°
Show the answer and explanation

Answer: B (54°)

Explanation

Draw a line through R parallel to ST and PQ. It splits the reflex angle into (180° − y), co-interior with y at S, and 72°, alternate to ∠RQP. So (180° − y) + 72° = 198°, giving y = 54°.