Q. 8

# The angles of a triangle are in the ratio 2: 3: 4. Find the angles of the triangle.

It is given to us –

The angles of a triangle are in the ratio 2: 3: 4.

We have to find the angles of the triangle.

Let us draw a ΔABC. Since the angles of the triangle is in the ratio 2: 3: 4, we can say that

A:B:C = 2:3:4

Let us assume,

A = 2x, B = 3x, and C = 4x - - - - (i)

We know that the sum of the three angles of a triangle is equal to 180°.

A + B + C = 180°

2x + 3x + 4x = 180° [From equation (i)]

9x = 180°

x = 20°

Substituting the value of x = 20° in equation (i), we get

A = 2x = 2 × 20° = 40°,

B = 3x = 3 × 20° = 60°, and

C = 4x = 4 × 20° = 80°

Thus, the angles of the triangle are 40°, 60°, and 80°.

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