Question

What angles must be congruent to QPS?

Answer 1

angle qts and angle rps

Answer 2

QTS & TQS

Explanation:

so as PQ=QT is given & QS is an common side, you can take the triangle PQS & TQS as isosceles triangles.

so then the angles PSQ=QST becoz the angles opposite to equal sides of an isosceles triangle are also equal in measures.

PQ=QT (given)

QS = common side

PSQ=QST (the angles opposite to equal sides of an isosceles triangle are also equal in measures.)

Therefore PQS is congruent to QTS (S.S.A)