In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS...
MATHEMATICS
WAEC 2004
In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS
- A. 35°
- B. 70°
- C. 100°
- D. 125°
Correct Answer: D. 125°
Explanation
∠PSQ = 90° (angle in a semi-circle)
(when SR is joined to SP)
∠SPQ = 180 – (90+35) = 180 – 125 = 55°
∠QRS + ∠SPQ = 180° (opposite angles in a cyclic quad is supplementary)
∠QRS = 180° - 55°
= 125°
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