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In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find...

Mathematics
WAEC 2023

In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find ∠ORS.

  • A. \(56^0\)
  • B. \(28^0\)
  • C. \(76^0\)
  • D. \(62^0\)
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Correct Answer: Option D
Explanation

∠SOR = 2 × 28° = 56° (angle at the centre is twice the angle at the circumference)
From ∆SOR
|OS| = |OR| (radii)
So, ∆SOR is isosceles.

ORS = \(\frac{180^0 -  56^0}{2} = \frac{124^0}{2}\)    ( base angles of isosceles triangle are equal)

∴ ∠ORS = 62°

 


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