In the diagram above, M, N, R are points on the circle centre O. ∠ORN = 48° and ∠RNM = 124°. Find ∠OMN.
Attached Figure / Diagram
A
\(58^0\)
B
\(64^0\)
C
\(48^0\)
D
\(76^0\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Reflex ∠MOR = 2 \times 124^\circ = 248^\circ (angle at the centre is twice the angle at the circumference)
∠MOR = 360^\circ - 248^\circ = 112^\circ (sum of angle at a point is 360^\circ)
∠OMN = 360^\circ - (124^\circ+ 48^\circ + 112^\circ) (sum of angles in a quadrilateral is 360^\circ)
= 360^\circ - 284^\circ
∴ ∠OMN = 76^\circ
Source: WAEC / JAMB / NECO Classroom Archive (Record #68980)