Question

Show that the angles of an epuilateral triangle are 60° each​

Answer 1

Answer:

In ∆ABC,

AB = AC = BC.

∴ ∠A = ∠B = ∠C,

let this is x°.

But sum of three angles is 180°.

∠A +∠B +∠C=180°

x+x+x=180°

3x=180°

x=180°÷3

x=60°

∴ ∠A =60°

∠B = 60°

∠C =60°

Step-by-step explanation:

hope it will help you

Answer 2

Step-by-step explanation:

Given:

ΔABC is an equilateral triangle

To prove:-

∠A = ∠B = ∠C = 60°

Solution:-

AB = BC = AC (∵ ΔABC is an equilateral triangle)

Since, angles opposite to equal sides are equal

AB = BC

∴ ∠A = ∠C

BC = AC

∴ ∠A = ∠B

AB = AC

∴  ∠B = ∠C

∠A = ∠B = ∠C

By angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

∠A + ∠A + ∠A = 180° (∵ ∠A = ∠B = ∠C)

3∠A = 180°

∠A = 180° ÷ 3

∠A = 60°

∴ ∠A = ∠B = ∠C = 60°

Hence proved