Question

Happy Diwali to all of you guys

Question is this

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

Answer 1

the sum of all sides of angle is 180°
equilateral triangles all sides all equal so it's all angles also equal by isosceles triangle therom
suppose angle 1+angle 2+angle 3 = 180°
suppose angles be x
so,x + x + x= 180°
3x=180°
x=180/3
x=60°
and showed

Answer 2

Hi there!

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Given :

ΔABC be an equilateral triangle.

∴ AB = BC = AC ( All sides of equilateral Δ are equal)

To prove :

∠A = ∠B = ∠C = 60°

Proof :

AB = AC

⇒ ∠C = ∠B (∠s opposite to equal sides are equal)...... (i)

Also, AC = BC

⇒ ∠B = ∠A (∠s opposite to equal sides are equal)...... (ii)

From (i) and (ii),

∠A = ∠B = ∠C.......... (iii)

In ΔABC,

∠A + ∠B + ∠C = 180° (Angle sum property of Δ)

⇒ ∠A + ∠A + ∠A = 180° [From eqⁿ (iii)]

⇒ 3∠A = 180°

⇒ ∠A = 180 / 3

⇒ ∠A = 60°

∴ ∠A = ∠B = ∠C = 60°

Hence, it is proved.

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Thanks for the question!

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