△ABC is similar to △RST . In addition, m∠C=76° and m∠S=3(m∠A) . What is m∠A ? Enter your answer in the box.
2 answers:
Answer:
∠A = 26°
Explanation:
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. In case of similar triangle, corresponding angles are congruent.
Angle ∠C = 76
So, ∠T = 76 because of corresponding angle.
Given that,
m∠S=3(m∠A)
We know that,
∠S ≅ ∠B
That means ∠B = 3 (∠A)
Sum of angles in a triangle = 180°
∠A + ∠B + ∠C = 180°
∠A + 3∠A + 76° = 180°
4∠A = 180° - 76°
4∠A = 104°
∠A =
∠A = 26°
Final answer.
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