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Question:

Prove that the angles of an equilateral triangle are 60° each.

Solution:

For an equilateral triangle, all sides are equal. Assuming an equilateral ΔABC, Then, AB=AC=BC. ⇒∠A=∠B=∠C (Angles opp. to equal sides are equal) For a triangle, by angle sum property, ∠A+∠B+∠C=180° Substituting ⇒∠A=∠B=∠C ∴∠A+∠A+∠A=180° ⇒3∠A=180° ⇒∠A=60° ∴∠A=∠B=∠C=60° So, each angle of an equilateral triangle is 60°.