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Given: ΔSTQ
ST=TQ
SD⊥TQ
m∠1=32°
find: m∠S, m∠T, m∠Q

Given: ΔSTQ ST=TQ SD⊥TQ m∠1=32° find: m∠S, m∠T, m∠Q-example-1
User Scot
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1 Answer

1 vote

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°

User Treetey
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