Question

2. Prove that each angle of an equilateral trias
60°. Hence show that every equilateral triang
is equiangular. What is the measure of each of
exterior angle of an equilateral triangle?
ionale​

Answer 1

Answer:

.As we know that all sides of a equilateral triangle are equal therefore

Step-by-step explanation:

In triangle ABC

AB=BC=AC

then angle C= angle A = angle B. (angle opposite to equal sides are also equal)

then,In triangle ABC

AngleA + AngleB +Angle C = 180 (Angle sum property of triangle)

3 Angle A= 180

Angle A= 60

As Angle A= angle B = angle C =60

Hence each angle is 60 and every equilateral triangle is equiangular.

Each exterior angle measures 120.

Answer 2

Solutions:

Let △ABC be an equilateral triangle. Then, AB = BC = CA.

Since, angles opposite to equal sides of a triangle are equal.

Hence, AB = BC and BC = CA

=> ∠C = ∠A and ∠A = ∠B

=> ∠A = ∠B = ∠C ............... (i)

Using angle sum property in△ABC, we obtain

∠A + ∠B + ∠C = 180°

=> ∠A + ∠A + ∠A = 180° .....[Using (i)]

=> 3∠A = 180°

=> ∠A = 60°

Hence, ∠A = ∠B = ∠C = 60°