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Question
Show that the angles of an equilateral triangle are 60° each.
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Solution
Let ABC be an equilateral triangle.
∴ AB = BC = AC …(A)
AB = BC ...[Taking first and second terms]
⇒ ∠C = ∠A …(i) ...[Angles opposite to equal sides]
Therefore,
AB = AC ...[Taking first and third terms of (A)]
⇒ ∠C = ∠B …(ii) ...[Angles opposite to equal sides]
From (i) and (ii) we get
∠A = ∠B = ∠C …(iii)
Now in △ABC …(iv)
∠A + ∠B + ∠C = 180° ...[Angle Sum Property]
⇒ ∠A + ∠A + ∠A = 180°
⇒ 3∠A = 180
⇒ ∠A = 60°
From (iii), ∠A = ∠B = ∠C
⇒ ∠A = ∠B = ∠C = 60°
Hence, each angle of an equilateral triangle is 60°.
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