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JAMB Mathematics 1989 Question 38

Question 38

Triangles and Quadrilaterals

In ΔPQR, the bisector of QP̂R meets QR at S. The line PQ is produced to V and the bisector of VQ̂S meets PS produced at T. If QP̂R = 46° and QŜT = 75°, calculate QT̂S

  1. A.41°
  2. B.52°
  3. C.64°
  4. D.82°
Show the answer and explanation

Answer: A (41°)

Explanation

Angle QPS = 23° and angle QSP = 180° − 75° = 105°, so the exterior angle VQS = 23° + 105° = 128° and angle TQS = 64°. In triangle QST, angle QTS = 180° − 75° − 64° = 41°.