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

Options

A. `60^(@)`
B. `40^(@)`
C. `80^(@)`
D. `20^(@)`

Answer

`````B````

Explanation

Given, the ratio of angles of a triangle is `2 : 4 : 3`
Let angles of a triangle be `/_A, /_B and /_C.`
`:." "/_A = 2X,/_B =3X and /_C = 3x`
In `Delta ABC, " " /_A + /_B + /_C = 180^(@)`
[sum of all the angles of a triangle is `180^(@)`]
`rArr " " 2x + 4x + 3x = 180^(@)`
`rArr " " 9x = 180^(@)`
`:. " " x = 180^(@)/9=20^(@)`
`:. " " /_A = 2x = 2xx20^(@) = 40^(@)`
`/_B = 4x = 4xx20^(@) = 80^(@)`
and `" " /_C = 3x = 3xx20^(@) = 60^(@)`
Hence, the smallest angle of a triangle is`40^(@)`.