Question

The largest angle of a triangle is twice the sum of the other two. The smallest is one fifth of the largest Determine all the angles in degrees.

Give step by step explanation

Please don't answer if you don't know​

Answer 1

let largest angle be

$\alpha$

and smallest angle be

$\beta$

and remaining angle be

$\gamma$

$now \: \alpha = 2( \beta + \gamma ) - - - - - eqn.1$

$\beta = \frac{ \alpha }{5}$

therefore,

$\alpha = 5 \beta$

and

$\alpha + \beta + \gamma = 180$

$5 \beta + \beta + \gamma = 180$

$6 \beta + \gamma = 180$

also from equation 1,

$5 \beta = 2( \beta + \gamma )$

$3 \beta = 2 \gamma$

$\gamma = \frac{3 \beta }{2}$

hence

$6 \beta + \frac{3 \beta }{2} = 180$

$\frac{12 \beta + 3 \beta }{2} = 180$

$15 \beta = 360$

$\beta = 24$

now

$\gamma = \frac{3 \times 24}{2} = 36$

$\alpha = 5 \times 24 = 120$

hence the angles are

$120 {}^{0} \\ 24 {}^{0} \\ 36 {}^{0}$