In the diagram, KS is a tangent to the circle centre O at R and...
MATHEMATICS
WAEC 2004
In the diagram, KS is a tangent to the circle centre O at R and ∠ROQ = 80°. Find ∠QRS.
- A. 90°
- B. 80°
- C. 50°
- D. 40°
Correct Answer: D. 40°
Explanation
QOP = 180 - 100(straight line angle) → 80°
OPQ and OQP are isosceles of 40° each.
∠QRS = ∠RPQ (theorem: angle in the alternate segment are equal)
∠RPQ = 40°
∠QRS = 40°
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