Question

an equilareral triangle has angles.if A+B+C=180°.then prove it.​

Answer 1

Answer:

IN AN EQUILATERAL TRIANGLE ALL ANGLES ARE EQUAL

Step-by-step explanation:

<A +<B+<C =180

3<A= 180

<A= 180÷ 3

<A=60 = <B = <C

therefore each angle is 60 and sum is 180

Answer 2

Answer:

Step-by-step explanation:

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.