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:
[tex](-13x+39)+(-4x+5)=180[/tex]
Open up the parentheses
[tex]-13x+39-4x+5=180[/tex]
Combine like terms
[tex]-17x+44=180[/tex]
Subtract 44 from both sides to isolate -17x
[tex]-17x+44-44=180-44\\-17x=136[/tex]
Divide both sides by -17
[tex]\frac{-17x}{-17} =\frac{136}{-17}\\x=-8[/tex]
Therefore, x is equal to -8. Now, use this to find the measure of each angle:
[tex]-4x+5\\= -4(-8)+5\\= 32+5\\= 37[/tex]
[tex]-13x+39\\= -13(-8)+39\\= 104+39\\=143[/tex]
(Alternatively, we can solve for one angle and then subtract it from 180 to solve for the other angle.)
I hope this helps!
