Angles of a triangle are in the ratio 2: 4: 3. The smallest angle of the triangle is

Question

Philoid · Accepted Answer

Let us draw a ΔABC.

It is given that the angles of the triangle are in the ratio 2: 4: 3.

Let us assume,

∠A = 2x, ∠B = 4x, ∠C = 3x - - - - (i)

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

So, ∠A + ∠B + ∠C = 180°

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

⇒ 9x = 180°

⇒ x = 20° - - - - (ii)

From equation (ii), we get

∠A = 2x = 2 × 20° = 40°

∠B = 4x = 4 × 20° = 80°

∠C = 3x = 3 × 20° = 60°

From above, we find that the smallest angle, ∠A is 40°.

Thus, option (B) is correct.

Option (A) is not correct. The smallest angle is not 60° this is because the smallest angle is ∠A which is 40°. So, the smallest angle of the triangle is not 60°.

Option (C) is not correct. ∠B measures 80° which is the largest angle of the triangle. So, the smallest angle of the triangle is not 80°.

Option (D) is not correct. 20° is not the correct angle for any of the angles of the triangle. So, the smallest angle of the triangle is not 20°.