Question 1044710

let the smallest angle be {{{alpha}}}
if the  angle {{{beta}}} of triangle is {{{two}}}{{{ times}}} smallest,than we have {{{beta=2*alpha}}}  and if {{{gamma}}}  three times smallest we have {{{gamma=3*alpha}}}

since the sum of all angles in triangle is {{{180}}}°, we have

 {{{alpha+beta+gamma=180}}}°........substitute {{{beta}}} and {{{gamma}}}

 {{{alpha+2*alpha+3*alpha=180}}}°

 {{{6*alpha=180}}}°

 {{{alpha=180/6}}}°

{{{alpha=30}}}°->the smallest angle

now find other two angles:

 {{{beta=2*alpha}}}-> {{{beta=2*30}}}°-> {{{beta=60}}}°
 
 {{{gamma=3*alpha}}}->{{{gamma=3*30}}}°->{{{gamma=90}}}°