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WAEC Mathematics 2006 Question 35

Question 35

Angles and Polygons

In the diagram, PQR is a straight line, QRST is a parallelogram, ∠TPQ = 72° and ∠RST = 126°. What type of triangle is ΔPQT?

Diagram for this question
  1. A.An equilateral triangle
  2. B.A right-angled triangle
  3. C.An isosceles triangle
  4. D.A scalene triangle
Show the answer and explanation

Answer: C (An isosceles triangle)

Explanation

In the parallelogram, ∠QRS = 180° − 126° = 54°, and TQ ∥ SR gives ∠PQT = 54° (corresponding angles). Then ∠PTQ = 180° − 72° − 54° = 54°. Two equal angles make ΔPQT isosceles.