Question

mPN=78 mQN=163.5 and mMQ=72. What is m angle PRM

Answer 1

we know that

The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.
∡PRM=(1/2)*[mPM+mQN]

mQN=163.5°
mPM=360-[163.5+72+78]-----> mPM=46.5°
∡PRM=(1/2)*[46.5+163.5]-----> 105 °

the answer is
∡PRM is 105 degrees