Since quadrilateral MNPQ is inscribed inside a circle, it means that it is a cyclic quadrilateral. For a cyclic quadrilateral, the opposite angles are supplementary. This means that their sum is 180 degrees.
This means that
M and P are opposite angles
angle M + angle P = 180 degrees
Also,
N and Q are opposite angles
angle N + angle Q = 180 degrees
We were told that segment MN is part of ray MR. This means that angle PNR is adjacent to angle PNM. The sum of the adjacent angles is 180 degrees
If angle PNR = 95 degrees, then,
angle PNM = 180 - 95 = 85 degrees
angle PNM is the same as angle N
We know that
angle N + angle Q = 180 degrees
85 + angle Q = 180
angle Q = 180 - 85
angle Q = 95 degrees
Thus, the correct option is
D) angle Q