In the diagram, triangle MNR is inscribed in circle MNR, and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR
A.
39º
B.
80º
C.
110º
D.
141º
Correct answer is B
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