Question

prove that an equilateral triangle is equiangular​

Answer 1

AB=AC⇒∠C=∠B ......(1)since angles opposite to equal sides are equal.

Also,AC=BC⇒∠B=∠A .....(2) since angles opposite to equal sides are equal.

From (1) and (2) we have

∠A=∠B=∠C ...(3)

In △ABC,

∠A+∠B+∠C=180

∘

(Angle sum property)

⇒∠A+∠A+∠A=180

∘

⇒∠A= 3(180°)

=60°

∴∠A=∠B=∠C=60

Hence Proved.