Question

5
Prove that in an equilateral triangle, each angle is of measure 60°​

Answer 1

Answer:-

Given:-

• ABC be an equilateral triangle

• AB=BC=AC (All sides of equilateral triangle are equal)

To prove:-

• ∠A = ∠B = ∠C = 60°

Proof:-

AB = AC

⇒∠C = ∠B----------(1)

(Angles opposite to equal sides are equal)

AC = BC

⇒∠B = ∠A----------(2)

From equation (1) & (2)

∠A = ∠B = ∠C----------(3)

In ΔABC,

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

⇒ ∠A + ∠A + ∠A = 180°  (from equation (3))

⇒3∠A = 180°

⇒∠A = 180°/3

⇒∠A = 60°

Therefore, ∠A = ∠B = ∠C = 60°

$\underline\boxed\red{Henceproved}$

Answer 2

Answer:

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°.

Hope it will help you..