Question

If the angles of a triangle are in the ratio 2 : 3 : 4 then the difference between the greatest and the smallest angle is _______

Answer 1

40°

Explanation;

Hint:

Given angles are in the ratio 2 : 3 : 4

Let the angles be 2x, 3x and 4x

Since sum of the angles of a triangle is 180°,

We get 2x + 3x + 4x = 180

∴ 9x = 180

∴ x = `180/9` = 20°

∴ The angles are 2x = 2 × 20 = 40°

3x = 3 × 20 = 60°

4x = 4 × 20 = 80°

∴ Difference between greatest and smallest angle is 80° – 40° = 40°