Show that the angles of an equilateral triangle are 60° each.

Solution:

Let's draw an equilateral triangle ABC as shown below.

Therefore,

AB = BC = AC

∴ ∠C = ∠A = ∠B (Angles opposite to equal sides of a triangle are equal)

Let ∠A = ∠B = ∠C be x. 

In △ ABC,

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

⇒ x + x + x = 180°

⇒ 3x = 180°

⇒ x = 60°

∴ ∠A = ∠B = ∠C = 60°

Hence, in an equilateral triangle, all interior angles are of measure 60°.

☛ Check: NCERT Solutions Class 9 Maths Chapter 7

Video Solution:

Show that the angles of an equilateral triangle are 60° each.

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.2 Question 8

Summary:

The angles of an equilateral triangle are 60° each as all interior angles are equal

☛ Related Questions:

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