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# 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:**

- ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that(i) ΔABE ≅ ΔACF(ii) AB = AC, i.e., ABC is an isosceles triangle.
- ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.
- ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠BCD is a right angle.
- ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

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