Hello! I am here with a few geometry questions today.

When you answer this question please be sure to explain your answer and show work.
Good luck! Have a great day!

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.