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WAEC Mathematics 2005 Question 10

Question 10

Circle Theorems

In the diagram, PR is a diameter, ∠PRQ = (3x − 8)° and ∠RPQ = (2y − 7)°. Express x in terms of y.

Diagram for this question
  1. A.x = (75 − 2y)/3
  2. B.x = (105 − 3y)/2
  3. C.x = (105 − 2y)/3
  4. D.x = (75 − 3y)/2
Show the answer and explanation

Answer: C (x = (105 − 2y)/3)

Explanation

∠PQR = 90° (angle in a semicircle), so (3x − 8) + (2y − 7) = 90, giving 3x = 105 − 2y and x = (105 − 2y)/3.