In the figure below, triangle qrs is isosceles, with qr sr.
note: picture not drawn to scale
if mspq = 33° and mqrs = 38°, what is mpqr?
118°
133°
138°
128°

128° Because triangle QRS is isosceles, angles QSR and SQR are congruent. The three angles in a triangle must total 180°, and since mQRS is 38°, the sum of mQSR and mSQR must be 142°. Since they are congruent, both angles are 71°. In triangle PQS, mQPS is 33° and mPSQ is 90°, meaning mSQP is 57°. (90+33=123; 180-123=57) mPQR can be found by adding mPQS (57°) and mSQR (71°). Therefore, mPQR=128°.