Question

In the figure below, triangle QRS is isosceles, with QR SR.

Answer 1

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°.