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JAMB Mathematics 1980 Question 12

Question 12

Angles and Polygons

In the figure below, if PT is parallel to RS, PQ = PT and angle SQT = 90°, find x

Diagram for this question
  1. A.35°
  2. B.50°
  3. C.55°
  4. D.70°
  5. E.80°.
Show the answer and explanation

Answer: D (70°)

Explanation

Let <PQT = <PTQ = y (isosceles). PT ∥ RS makes <P + x = 180°, so x = 2y. On the line at Q, <SQR = 90° − y, and in triangle QSR, 55° + x + 90° − y = 180°. So y = 35° and x = 70°.