In PQR, side QR is produced to a point S, and exterior angle PRS 100°. If RP RQ, then measure of PQR is

Correct option is A

Using the Exterior Angle Theorem:
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.  
In this case, the exterior angle PRS is 100°, and the two remote interior angles are PQR and PRQ.  
So, 100° = PQR + PRQ.
Using the properties of an isosceles triangle:
Since triangle PQR is isosceles with base PR, angles PQR and PRQ are equal.
Let's denote the measure of each of these angles as x.
So, 100° = x + x
Solving for x:
2x = 100°
x = 50°
Therefore, the measure of angle PQR is 50°.