Q1. In the figure given below, PQR is a triangle in which angle PQR is 50°. QR is parallel to PM. If QR = PR, then what is the value of angle RPM?
A 70°
B 80° Correct
C 100°
D 95°
Explanation
The figure marks angle PQR as 50°. Since QR = PR, triangle PQR is isosceles, so the angles opposite these equal sides are equal; hence angle QPR is also 50°. The remaining angle QRP is 180° - 50° - 50° = 80°. Because QR is parallel to PM, angle RPM equals the corresponding angle between PR and QR, which is 80°. The values 70°, 100° and 95° do not satisfy both the isosceles-triangle condition and the parallel-line angle relation.