from a handpicked tutor in LIVE 1-to-1 classes

# 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.

**☛ Related Questions:**

- The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju are twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
- One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II] [Hint: x +100 = 2 ( y -100), y +10 = 6 (x -10)]
- A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
- The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

visual curriculum