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

Solution:

According to the angle sum property of a triangle, sum of the measures of all the angles of a triangle is 180°.

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°

⇒ ∠A + ∠B + 3∠B = 180° [∵ ∠C = 3∠B]

⇒ ∠A + 4∠B = 180

⇒ x + 4y = 180 ...(2)

Multiplying equation (1) by 4, we obtain

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

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

x + 4y + 8x - 4y = 180 + 0

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°

☛ Check: NCERT Solutions Class 10 Maths Chapter 3

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

Summary:

If in △ABC, ∠C = 3∠B = 2(∠A + ∠B), the angles of the triangle are ∠A = 20°, ∠B = 40°, and ∠C = 120° respectively.

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