Answered

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°

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° class=

Answer :

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°.

Other Questions