In the diagram, triangle MNR is inscribed in circle MNR, and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR
Attached Figure / Diagram
A
39º
B
80º
C
110º
D
141º
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.
∠M = ∠R + ∠N
→ 141 = 41 + ∠N
∠N = 141 - 41 = 100º
∠QNR = 180 - 100 → 80º
Source: WAEC / JAMB / NECO Classroom Archive (Record #64851)