In a triangle ABC, `2/_A = 3/_B = 6/_C`. Then the smallest angle in the `DeltaABC` is

Options

A. `40^@`
B. `60^@`
C. `80^@`
D. none of these

Answer

A

Explanation

Let `6angleA=4angleB=3angleC=x`
`rArr angleA=(x)/(6),angleB=(x)/(4) and angleC=(x)/(3)`
`rArr (x)/(6)+(x)/(4)+(x)/(3)=180^(@) " " ( :. angleA +angle B +angle C =180^(@))`
`rArr 2x+3x+4x=180^(@)xx12`
`rArr9x=180^(@)xx12`
`rArrx=240^(@)`
`:. angleA=(x)/(6)=(240^(@))/(6)=40^(@)`
`:. angleB=(x)/(4)=(240^(@))/(4)=60^(@)`
`:. angleC=(x)/(3)=(240^(@))/(3)=80^(@)`