Question 934370



the largest angle of a triangle is {{{alpha}}}
the smallest angle is {{{beta}}}
the third angle is {{{gamma}}}

{{{alpha +beta+gamma=180}}}........eq.1

given:

The measure of the largest angle of a triangle is twice the measure of the smallest angle. 

=> {{{alpha=2beta}}}.....eq.2

The measure of the third angle is {{{10}}} degrees {{{less}}} than the measure of the largest angle.

 =>{{{gamma=alpha-10}}}.....eq.3...substitute  {{{2beta}}} for {{{alpha}}} 

{{{gamma=2beta-10}}}

 {{{2beta+beta+2beta-10=180}}}......eq.1...........solve for {{{alpha}}}

{{{5beta=180+10}}}

{{{5beta=190}}}.

{{{beta=190/5}}}

{{{highlight(beta=38)}}}

go to {{{alpha=2beta}}}.....eq.2 plug in {{{38}}} for {{{beta}}}

{{{alpha=2*38}}}

{{{highlight(alpha=76)}}}

and

{{{gamma=alpha-10}}}.....eq.3.

{{{gamma=76-10}}}

{{{highlight(gamma=66)}}}