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3 years ago

△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.

Mathematics

2 answers:

Oksi-84 [34.3K]3 years ago

8 0

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 = $\frac{104}{4}$

∠A = 26°

Final answer.

san4es73 [151]3 years ago

5 0

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