Question

Angle A and angle B are supplementary (180°)

and their measures have a difference of 50°. What
are the measures of the angles? Generalize
your method.

Answer 1

65 and 115 degrees.

Explanation:

Set up and define the variables.

Angle A: x

Angle B: x + 50 {this is because one is 50 degrees more than the other}

Set up equation.

- {supplementary angles have a combined sum of 180}

x + x + 50 = 180

Solve equation.

2x + 50 = 180

2x = 130

x = 65

Substitute answers into original setup of variables.

A: 65

B: 65+50= 115

Answer 2

65° and 115°

Explanation:

Given: Angle A and Angle B are supplementary

Let x represent Angle A. Since the angles have a difference of 50, Angle B would be x+50.

We are given that Angle A and Angle B are supplementary which means they add up to 180°. We can use this information to set up an equation.

Angle A + Angle B = 180

Substitute the variables we used to represent Angle A and B into the equation

x+x+50=180

Combine like terms

2x+50=180

Subtract both sides by 50

2x=130

Divide both sides by 2

x=65

x+50=65+50=115

The measure of the angles are 65° and 115°