Question 1136556

Three angles in a triangle add up to {{{180}}} degrees. 

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


if the largest angle {{{alpha}}} is two degrees more than twice
the second largest angle {{{beta}}}, we have

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

if the smallest angle {{{gamma}}} is {{{18}}} degrees less than the second largest angle {{{beta}}}, we have

{{{gamma=beta-18}}}......eq.3

go back to eq.1

{{{alpha +beta+gamma=180}}}..........eq.1, substitute {{{alpha}}} and {{{gamma}}} 

{{{2beta+2 +beta+beta-18=180}}}.......solve for {{{beta}}}

{{{4beta-16=180}}}

{{{4beta=180+16}}}

{{{4beta=196}}}

{{{beta=196/4}}}

{{{beta=49}}}


go to {{{alpha=2beta+2}}}..........eq.2

{{{alpha=2*49+2}}}

{{{alpha=100}}}



go to {{{gamma=beta-18}}}......eq.3

{{{gamma=beta-18}}}

{{{gamma=49-18}}}

{{{gamma=31}}}

the measure of all three angles: {{{alpha=100}}}°, {{{beta=49}}}°, {{{gamma=31}}}°