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.
\(76^0\)
Correct answer is D
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°