Question 922923


In triangle {{{JKL}}}, {{{JK}}} is congruent to {{{KL}}}=> then we have an isosceles triangle which means angles {{{J}}} and {{{L}}} are congruent


given: 
angle {{{J=2x-y}}}
angle {{{L=x+2y }}}
angle {{{K=2x+2y}}}

{{{J=L}}}

{{{2x-y=x+2y}}}

{{{2x-x=y+2y}}}

{{{x=3y}}} 

=> {{{J=2*3y-y}}}=> {{{J=6y-y}}}=> {{{J=5y}}} 

=>{{{L=x+2y }}}=>{{{L=3y+2y }}}=>{{{L=5y }}}and

=>{{{K=2x+2y}}}=>{{{K=2*3y+2y}}}=>{{{K=6y+2y}}}=>{{{K=8y}}}

now, we also know that the sum of all angles in triangle is {{{180}}}

{{{J+L+K=180}}}

{{{5y+5y+8y=180}}} ....solve for {{{y}}}

{{{18y=180}}}

{{{y=180/18}}}

{{{highlight(y=10)}}}

now find {{{x}}}

{{{x=3y}}} 

{{{x=3*10}}} 

{{{highlight(x=30)}}} 


since you know {{{x}}} and {{{y}}}, you can find the measure of the angles too:

{{{J=5y}}}=>{{{J=50}}}

{{{L=5y}}}=>{{{L=50}}}

{{{K=8y}}}=>{{{K=80}}}