Test 7 Section 3 #17

The first thing to do on any find-the-measure-of-a-certain-angle problem is complete any 180°s you can. In this case, triangle *PQR* can be completed (the measure of angle *PRQ* must be 50°) and can be completed (the measure of angle *MPR* must be 120°).

From there, you’re almost home. The question tells you that *MP* = *PR*, so you know that triangle *MPR* is isosceles. That means that angles *PMR* and *PRM* must be congruent! Because that triangle already has a 120° angle in it, the two unknowns must add up to 60°. Because they must be congruent, they must each be 30°.

Therefore, the measure of angle *QMR* is 30°.