Question

Hello!

Answer 1

Triangle PQR is isosceles. It's a unique side-angle-side triangle (both PQ and QR are congruent), so the other two angles in it are congruent and have the same measure. The interior angles of any triangle sum to 180° in measure, so

64° + m∠QPR + m∠PRQ = 180°

2 m∠QPR = 116°

m∠QPR = 58°

Angles PRQ and TRS form a vertical pair, so they are also congruent and m∠TRS = 58°.

This in turn means triangle RST is isosceles (again due to the side-angle-side postulate) so that angles RST and RTS have the same measure. Then

58° + m∠RST + m∠RTS = 180°

2 m∠RST = 122°

m∠RST = 61°

making the answer B.