Question

Given: ΔSTQ, ST = TQ ST ⊥ TQ m∠1=32º. Find: m∠S, m∠T, m∠Q

Answer 1

 m∠S = 58º , m∠T=64º, m∠Q=58º

Answer 2

M∠S = 45°; m∠T = 90°; m∠Q = 45°

Explanation
Since ST⊥TQ, this means that m∠T = 90°.

This means that m∠S+m∠Q = 180-90 = 90°.

Since ST = TQ, this means that the other two angles, formed by the legs and the hypotenuse, must be congruent.  90/2 = 45° for each angle.