SOLUTION: Find the measure of each unknown angle

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Question 119245: Find the measure of each unknown angle
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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Remember, supplementary angles add to 180. So these angles are the bottom left angles



Start with the given equation



Combine like terms on the left side


Add 22 to both sides


Combine like terms on the right side


Divide both sides by 4 to isolate x



Reduce

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Answer:
So our answer is (which is approximately in decimal form)


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Now plug in into to find the angle

Plug in


Simplify

So the first interior angle is 129.5 degrees

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Now plug in into to find the angle

Plug in


Simplify

So the second interior angle is 91 degrees


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





So

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Now into to find the angle

Plug in


Simplify

So the third interior angle is 65.5 degrees


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





So

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

Angle1+Angle2+Angle3+Angle4=360


Plug in the given info. These are the angles that were previously solved for.


Combine like terms


Subtract 286 from both sides


Combine like terms on the right side


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





So

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Answer:
So our answer is

So the fourth interior angle w is 74 degrees




Summary:

So we have the following angles:
, , , , , and









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