Hello!
[tex]\large\boxed{m1 = 40^{o}, m2 = 140^{o}}[/tex]
Supplementary angles sum up to 180°, therefore:
m∠1 + m∠2 = 180°
x - 17 + x + 83 = 180°
Combine like terms:
2x + 66 = 180°
Subtract 66 from both sides:
2x = 114°
Divide both sides by 2:
x = 57°
Find the measures of both angles using this value:
m∠1 = 57 - 17 = 40°
m∠2 = 57 + 83 = 140°
Answer:
Angle 1: 40 degrees
Angle 2: 140 degrees
Step-by-step explanation:
1. Supplementary angles have a sum of 180 degrees. That being said, add the two expressions together and set them equal to 180. Then solve for x.
x-17+x+83=180 (combine like terms)
2x+66=180 (subtract 66 from both sides)
2x=114 (divide by 2)
x = 57
2. Now that you have determined that x is 57, plug that back into each expression to figure out the measurements for both angles.
Angle 1: 57 - 17 = 40.
Angle 2: 57+83 = 140
3. You can check your work by adding the two measurements and making sure that they equal 180 degrees. 40 + 140 does equal 180, and that is how you know solved it correctly. :)
