passwella.
Menu

JAMB Mathematics 1999 Question 27

Question 27

Circle Theorems

In the figure above, PQRS is a circle with ST||RQ. Find the value of x if PT = PS.

Diagram for this question
  1. A.70°
  2. B.55°
  3. C.40°
  4. D.35°
Show the answer and explanation

Answer: B (55°)

Explanation

Opposite angles of cyclic quadrilateral PQRS add to 180°, so ∠SPT = 180° − 110° = 70°. Triangle PST is isosceles, so ∠PTS = (180° − 70°)/2 = 55°. Since ST ∥ RQ, x = ∠PTS = 55° (corresponding angles).