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:

80°

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°