Question

What is the measure of each angle in the diagram

Answer 1

The answer is 37 degrees and 143 degrees

Answer 2

Answer:

37° and 143°

Step-by-step 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

$\frac{-17x}{-17} =\frac{136}{-17}\\x=-8$

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!