Question

What is the measure of each angle in the diagram

Answer 1

the answer is 37 degrees and 143 degrees

Answer 2

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!