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Question
Prove that each angle of an equilateral triangle is 60°.
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Solution
Given to prove that each angle of an equilateral triangle is 60°
Let us consider an equilateral triangle ABC
Such that AB= BC= CA
Now,
AB=BC ⇒ ∠A=∠C ................(1) [Opposite angles to equal sides are equal]
and BC = AC ⇒∠B = ∠A ……..(2)
From (1) and (2), we get
∠A = ∠B = ∠C ..............(3)
We know that
Sum of angles in a triangle =180°
⇒∠A+∠B+∠C=180°
⇒ ∠A+∠A+∠A=180°
⇒3 ∠A=180°
⇒ `∠A=(180°)/3=60°`
∴∠S=∠B=∠C=60°
Hence, each angle of an equilateral triangle is 60°.
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