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) About Me  (Show Source):
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Remember, supplementary angles add to 180. So x%2B3x-22=180 these angles are the bottom left angles



x%2B3x-22=180 Start with the given equation



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


4x=180%2B22Add 22 to both sides


4x=202 Combine like terms on the right side


x=%28202%29%2F%284%29 Divide both sides by 4 to isolate x



x=101%2F2 Reduce

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Answer:
So our answer is x=101%2F2 (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%2850.5%29-22 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%2850.5%29-10 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%2B15 to find the angle

50.5%2B15 Plug in x=50.5


65.5 Simplify

So the third interior angle x%2B15 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%2B91%2B65.5%2Bw=360 Plug in the given info. These are the angles that were previously solved for.


286%2Bw=360 Combine like terms


w=360-286Subtract 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%2B15=65.5, z=114.5, w=74 and u=106