Question 1008069

In triangle {{{XYZ}}}, the measure of all three angles is:

{{{X+Y+Z=180}}}.....eq.1

if the measure of angle {{{X}}} is {{{eight}}} times the {{{sum}}} of the measures of angles {{{Y}}} and {{{Z}}}, we have
{{{X=8(Y+Z)}}}.....eq.2

if the measure of angle {{{Y}}} is {{{three}}} times the measure of angle {{{Z}}}, then we have

{{{Y=3Z}}}.....eq.3....substitute in eq.2

{{{X=8(3Z+Z)}}}.....eq.2

{{{X=8*4Z}}}

{{{X=32Z}}}

now we know that {{{X=32Z}}} and {{{Y=3Z}}}; substitute it in eq.1

{{{X+Y+Z=180}}}.....eq.1

{{{32Z+3Z+Z=180}}} .....solve for {{{Z}}}

{{{36Z=180}}}

{{{Z=180/36}}}

{{{highlight(Z=5)}}}

now we can find the measure of {{{X}}} and {{{Y}}}

{{{X=32Z}}} =>{{{X=32*5}}} =>{{{highlight(X=160)}}}

and {{{Y=3Z}}}=>{{{Y=3*5}}}=>{{{highlight(Y=15)}}}