Question 119555
For any quadrilateral, the sum of the 4 angles is 360 degrees. So in this case, {{{J+K+L+M=360}}}



{{{J+K+L+M=360}}} Start with the given equation 



{{{x+2x+2x+10+3x-5=360}}} Plug in {{{J=x}}}, {{{K=2x}}}, {{{L=2x+10}}},and {{{M=3x-5}}}




{{{8x+5=360}}} Combine like terms on the left side



{{{8x=360-5}}}Subtract 5 from both sides



{{{8x=355}}} Combine like terms on the right side



{{{x=(355)/(8)}}} Divide both sides by 8 to isolate x




{{{x=355/8}}} Reduce




Since {{{x=355/8}}} (which is {{{x=44.375}}} in decimal form), our first angle is {{{J=44.375}}}




Since {{{x=44.375}}}, we can plug this into {{{K=2x}}} to get


{{{K=2(44.375)=88.75}}}


So our second angle is {{{K=88.75}}}




Since {{{x=44.375}}}, we can plug this into {{{L=2x+10}}} to get


{{{L=2(44.375)+10=88.75+10=98.75}}}


So our third angle is {{{L=98.75}}}



Since {{{x=44.375}}}, we can plug this into {{{M=3x-5}}} to get


{{{M=3(44.375)-5=133.125-5=128.125}}}


So our fourth angle is {{{M=128.125}}}


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Answer:



So the measures of the four angles are:



{{{J=44.375}}}, {{{K=88.75}}}, {{{L=98.75}}}, and {{{M=128.125}}}




Check:


{{{J+K+L+M=360}}} Start with the given equation


{{{44.375+88.75+98.75+128.125=360}}} Plug in {{{J=44.375}}}, {{{K=88.75}}}, {{{L=98.75}}}, and {{{M=128.125}}}


{{{360=360}}} Add. Since the two sides of the equation are equal, this verifies our answer.