The measure of angle RNQ is 50 degrees
In the image provided, angle RNQ is an inscribed angle. An inscribed angle is an angle that is formed by two chords that intersect inside a circle. The measure of an inscribed angle is half the measure of its intercepted arc.
The intercepted arc for angle RNQ is the arc PR, which measures 100 degrees. Therefore, the measure of angle RNQ is:
angle RNQ = 1/2 * arc PR
= 1/2 * 100 degrees = 50 degrees
Therefore, the measure of angle RNQ is 50 degrees.