PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at M. If $\angle QMR=40°$, then $\angle P$ is:
Answer & explanation
Correct answer: option 4
The exterior angle of a given triangle equals the sum of the opposite interior angles of that triangle.
Here Exterior angle is R and interior angle is P and Q
Thus, Exterior Angle R = interior angle (P+Q)
R = P+Q .....(1)
In new formed triangle MQR, by two given bisectors, interior angles are M and half of Q and exterior angle is half of R
M + 0.5Q = 0.5R
40 + 0.5Q = 0.5(P+Q)
40 + 0.5Q = 0.5P + 0.5Q
0.5P = 40
P = 80
The correct answer is Option (4) → 80°