#### Answer

R$=82^{\circ}$, N$=12^{\circ}$ and M$=86^{\circ}$

#### Work Step by Step

Since the triangles are similar, corresponding angles also have the same measure.
Since P corresponds to R and P measures 82$^{\circ}$, R also measures 82$^{\circ}$.
Since N corresponds to Q and Q measures 12$^{\circ}$, N also measures 12$^{\circ}$.
Since M corresponds to S and S measures 86$^{\circ}$, M also measures 86$^{\circ}$.