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What is the measure of each angle in the diagram

What is the measure of each angle in the diagram-example-1
User Boroboris
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the answer is 37 degrees and 143 degrees
User Mijin
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5 votes

Answer:

37° and 143°

Explanation:

Hi there!

These labeled angles are corresponding angles, meaning they have a sum of 180 degrees (we can tell because the line segments they join make a "C" shape).

Knowing this, we can construct the following equation to solve for x:


(-13x+39)+(-4x+5)=180

Open up the parentheses


-13x+39-4x+5=180

Combine like terms


-17x+44=180

Subtract 44 from both sides to isolate -17x


-17x+44-44=180-44\\-17x=136

Divide both sides by -17


(-17x)/(-17) =(136)/(-17)\\x=-8

Therefore, x is equal to -8. Now, use this to find the measure of each angle:


-4x+5\\= -4(-8)+5\\= 32+5\\= 37


-13x+39\\= -13(-8)+39\\= 104+39\\=143

(Alternatively, we can solve for one angle and then subtract it from 180 to solve for the other angle.)

I hope this helps!

User Brandrally
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