Explanation:
Measure of arc QS is the angle measure of P*2
arc QS is 114
Measure of arc QR is 114-41, 73
Since M<Q has to be 1/2 * 137, this makes angle M<Q equal to 68.5, and since the angles in a triangle add up to 180, the angle measure of angle S is 54.5.
Now lets treat this like a quadrilateral.
Since the angles in a quadrilateral add up to 360, and we know the angle measures of P, Q, and S, we can say that the angle measure of R of quadrilateral PQRS is equal to 360-(57+68.5+54.5), which makes angle R 180.
M<Q = 68.5
M<R = 180
M<S = 54.5