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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 = 80º. Find ∠QRS.

  • A. 90o
  • B. 80o
  • C. 50o
  • D. 40o
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Correct Answer: Option D
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 = 40º
∠QRS = 40º

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