Mathematics
In triangle ABC; AB = AC and ∠A : ∠B = 8 : 5; find angle A.
Triangles
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Answer
Given,
⇒ ∠A : ∠B = 8 : 5
Let ∠A = 8x and ∠B = 5x.
In △ ABC,
⇒ AB = AC (Given)
⇒ ∠C = ∠B = 5x (Angles opposite to equal sides are equal)
By angle sum property of triangle,
⇒ ∠A + ∠B + ∠C = 180°
⇒ 8x + 5x + 5x = 180°
⇒ 18x = 180°
⇒ x = = 10°.
⇒ ∠A = 8x = 8 × 10° = 80°.
Hence, ∠A = 80°.
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