Question 119245
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Remember, supplementary angles add to 180. So {{{x+3x-22=180}}} these angles are the bottom left angles




{{{x+3x-22=180}}} Start with the given equation




{{{4x-22=180}}} Combine like terms on the left side



{{{4x=180+22}}}Add 22 to both sides



{{{4x=202}}} Combine like terms on the right side



{{{x=(202)/(4)}}} Divide both sides by 4 to isolate x




{{{x=101/2}}} Reduce


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Answer:

So our answer is {{{x=101/2}}}  (which is approximately {{{x=50.5}}} in decimal form)



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Now plug in {{{x=50.5}}} into {{{3x-22}}} to find the angle 


{{{3(50.5)-22}}} Plug in {{{x=50.5}}} 



{{{129.5}}} Simplify


So the first interior angle {{{3x-22}}} is 129.5 degrees


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Now plug in {{{x=50.5}}} into {{{2x-10}}} to find the angle 


 {{{2(50.5)-10}}} Plug in {{{x=50.5}}} 



 {{{91}}} Simplify


So the second interior angle  {{{2x-10}}}  is 91 degrees



Now subtract that answer from 180 to solve for the exterior angle y



{{{180-91=89}}}



So {{{y=89}}}


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Now {{{x=50.5}}} into {{{x+15}}} to find the angle 


 {{{50.5+15}}} Plug in {{{x=50.5}}} 



 {{{65.5}}} Simplify


So the third interior angle  {{{x+15}}}  is 65.5 degrees



Now subtract that answer from 180 to solve for the exterior angle z



{{{180-65.5=114.5}}}



So {{{z=114.5}}}


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Since the sum of the 4 angles in any quadrilateral is 360 degrees, this means 


Angle1+Angle2+Angle3+Angle4=360



{{{129.5+91+65.5+w=360}}} Plug in the given info. These are the angles that were previously solved for.



{{{286+w=360}}} Combine like terms



{{{w=360-286}}}Subtract 286 from both sides



{{{w=74}}} Combine like terms on the right side



Now subtract that answer from 180 to solve for the exterior angle u



{{{180-74=106}}}



So {{{u=106}}}


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Answer:

So our answer is {{{w=74}}} 


So the fourth interior angle w is 74 degrees





Summary:


So we have the following angles:

{{{x=50.5}}}, {{{3x-22=129.5}}} {{{2x-10=91}}}, {{{y=89}}}, {{{x+15=65.5}}}, {{{z=114.5}}}, {{{w=74}}} and {{{u=106}}}