# In △ABC, ∠C = 3∠B = 2(∠A + ∠B) . Find the three angles

**Solution:**

The sum of the measures of all angles of a triangle is 180°. --- (Angle Sum Property)

Let the measurement of ∠A = x°

And the measurement of ∠B = y°

Using the information given in the question,

∠C = 3∠B = 2 (∠A + ∠B)

⇒ 3∠B = 2 (∠A + ∠B)

⇒ 3y = 2 ( x + y )

⇒ 3y = 2x + 2 y

⇒ 2x - y = 0 ....(1)

We know that the sum of the measures of all angles of a triangle is 180°. Therefore,

∠A + ∠B + ∠C = 180° [∵ ∠C = 3∠B]

∠A + ∠B + 3∠B = 180°

∠A + 4∠B = 180°

x + 4 y = 180°

Multiplying equation (1) by 4, we obtain

8x - 4 y = 0 ....(3)

Adding equations (2) and (3), we obtain

9x = 180

x = 20

Substituting x = 20 in equation (1), we obtain

2 × 20 - y = 0

y = 40

Therefore,

∠A = x° = 20°

∠B = y° = 40°

∠C = 3∠B = 3 × 40° = 120°

**Video Solution:**

## In △ABC, ∠C = 3∠B = 2(∠A + ∠B) . Find the three angles

### Class 10 Maths NCERT Solutions - Chapter 3 Exercise 3.7 Question 5:

In △ABC, ∠C = 3∠B = 2(∠A + ∠B) . Find the three angles

If the angles of triangles are such that angle C = 3B and 3B = 2 ( A + B ). The angles of the triangle are such that A = 20°, B = 40°, C = 120°