If the angles of a triangle are in the ratio 2 : 3 : 4 then the differ

1.	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» 40° Given angles are in the ratio 2 : 3 : 4 Let the angles be 2x, 3x & 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 x 20 = 40° 3x = 3 x 20 = 60° 4x = 4 x 20 = 80° ∴ Difference between greatest & smallest angle is 80° – 40° = 40°

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»

40°

Given angles are in the ratio 2 : 3 : 4

Let the angles be 2x, 3x & 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 x 20 = 40°

3x = 3 x 20 = 60°

4x = 4 x 20 = 80°

∴ Difference between greatest & smallest angle is

80° – 40° = 40°