In the diagram above, M, N, R are points on the circle centre O. &ang;ORN =...

In the diagram above, M, N, R are points on the circle centre O. ∠ORN =...

Mathematics

WAEC 2023

In the diagram above, M, N, R are points on the circle centre O. ∠ORN = 48° and ∠RNM = 124°. Find ∠OMN.

A. \(58^0\)
B. \(64^0\)
C. \(48^0\)
D. \(76^0\)

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Correct Answer: Option D

Explanation

Reflex ∠MOR = 2 × 124° = 248° (angle at the centre is twice the angle at the circumference)
∠MOR = 360° - 248° = 112° (sum of angle at a point is 360°)
∠OMN = 360° - (124°+ 48° + 112°) (sum of angles in a quadrilateral is 360°)
= 360° - 284°
∴ ∠OMN = 76°

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