Question

<1 and <2 are supplementary angles, m<1 = x - 17, and m<2 = x+83. Find the measure of each angle.

Answer 1

Angle 1: 40 degrees

Angle 2: 140 degrees

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. :)

Answer 2

Hello!

`\large\boxed{m1 = 40^(o), m2 = 140^(o)}`

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°