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

Question

Philoid · Accepted Answer

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°.