Answer:
∠ S = 58° , ∠ T = 64° , ∠ Q = 58°
Explanation:
the sum of the 3 angles in Δ DQS = 180° , that is
∠ Q + ∠ 1 + 90° = 180°
∠ Q + 32° + 90° = 180°
∠ Q + 122° = 180° ( subtract 122° from both sides )
∠ Q = 58°
given ST = TQ , then Δ STQ is isosceles with base angles congruent, that is
∠ S = ∠ Q = 58°
the sum of the 3 angles in Δ STQ = 180° , that is
∠ T + ∠ S + ∠ Q = 180°
∠ T + 58° + 58° = 180°
∠ T + 116° = 180° ( subtract 116° from both sides )
∠ T = 64°