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Question
Find all the angles of an equilateral triangle.
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Solution
Let ABC be an equilateral triangle such that AB = BC = CA
We have, AB = AC ⇒ ∠C = ∠B ...[Angle opposite to equal sides are equal]
Let ∠C = ∠B = x° ...(i)
Now, BC = BA
⇒ ∠A = ∠C ...(ii) [Angles opposite to equal sides are equal]
From equations (i) and (ii),
∠A = ∠B = ∠C = x
Now, in ΔABC, ∠A + ∠B + ∠C = 180° ...[By angle sum property of a triangle]
⇒ x + x + x = 180°
⇒ 3x = 180°
∴ x = 60°
Hence, ∠A = ∠B = ∠C = 60°
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