Supplementary Angles

Supplementary angles are two angles whose measures add up to .

The two angles of a linear pair , like in the figure below, are always supplementary.

But, two angles need not be adjacent to be supplementary. In the next figure, are supplementary, because their measures add to .

Example 1:

Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.

Let the measure of one of the supplementary angles be .

Measure of the other angle is times .

So, measure of the other angle is .

If the sum of the measures of two angles is , then the angles are supplementary.

So,

Simplify.

To isolate , divide both sides of the equation by .

The measure of the second angle is,

So, the measures of the two supplementary angles are and .

Example 2:

Find if are supplementary, , and .

The sum of the measures of two supplementary angles is .

So,

Substitute for and for .

Combine the like terms. We get:

Add to both the sides. We get:

Divide both the sides by .

Simplify.

To find , substitute for in .

Simplify.

So, .

To find , substitute for in .

Simplify.

So, .

See also complementary angles .