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Mathematics

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

Triangles

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Answer

Show that the angles of an equilateral triangle are 60° each. NCERT Class 9 Mathematics CBSE Solutions.

Construct a triangle ABC with AB = BC = AC.

In △ ABC,

AB = BC = AC

We know that,

Angles opposite to equal sides of a triangle are equal.

∴ ∠C = ∠A = ∠B = x (let)

In △ ABC,

⇒ ∠A + ∠B + ∠C = 180° (Angle sum property of a triangle)

⇒ x + x + x = 180°

⇒ 3x = 180°

⇒ x = 180°3\dfrac{180°}{3}

⇒ x = 60°.

∴ ∠A = ∠B = ∠C = 60°.

Hence, proved that the angles of an equilateral triangle are 60° each.

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