What if you were given two supplementary angles? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of supplementary angles to solve problems like this one.

### Watch This

CK-12 Foundation: Chapter1SupplementaryAnglesA

James Sousa: Supplementary Angles

### Guidance

Two angles are **supplementary** when they add up to \begin{align*}180^\circ\end{align*}. Supplementary angles do not have to be congruent or touching.

#### Example A

The two angles below are supplementary. If \begin{align*}m \angle MNO = 78^\circ\end{align*} what is \begin{align*}m \angle PQR\end{align*}?

Set up an equation.

\begin{align*}78^\circ + m \angle PQR = 180^\circ\\ m \angle PQR = 102^\circ\end{align*}

#### Example B

What are the measures of two congruent, supplementary angles?

Supplementary angles add up to \begin{align*}180^\circ\end{align*}. Congruent angles have the same measure. Divide \begin{align*}180^\circ\end{align*} by 2, to find the measure of each angle.

\begin{align*}180^\circ \div 2 = 90^\circ\end{align*}

So, two congruent, supplementary angles are right angles, or \begin{align*}90^\circ\end{align*}.

#### Example C

Name one pair of supplementary angles in the diagram below.

One example is \begin{align*} \angle INM\end{align*} and \begin{align*} \angle MNL\end{align*}.

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1SupplementaryAnglesB

### Vocabulary

Two angles are ** supplementary** when they add up to \begin{align*}180^\circ\end{align*}.

### Guided Practice

Find the measure of an angle that is supplementary to \begin{align*}\angle ABC\end{align*} if \begin{align*}m \angle ABC\end{align*} is

1. \begin{align*}45^\circ\end{align*}

2. \begin{align*}118^\circ\end{align*}

3. \begin{align*}32^\circ\end{align*}

4. \begin{align*}x^\circ\end{align*}

**Answers:**

1. \begin{align*}135^\circ\end{align*}

2. \begin{align*}62^\circ\end{align*}

3. \begin{align*}148^\circ\end{align*}

4. \begin{align*}180-x^\circ\end{align*}

### Interactive Practice

### Practice

Find the measure of an angle that is supplementary to \begin{align*}\angle ABC\end{align*} if \begin{align*}m\angle ABC\end{align*} is:

- \begin{align*}112^\circ\end{align*}
- \begin{align*}15^\circ\end{align*}
- \begin{align*}97^\circ\end{align*}
- \begin{align*}81^\circ\end{align*}
- \begin{align*}57^\circ\end{align*}
- \begin{align*}(x-y)^\circ\end{align*}
- \begin{align*}(x+y)^\circ\end{align*}

Use the diagram below for exercises 8-9. Note that \begin{align*}\overline{NK} \perp \overleftrightarrow{IL}\end{align*}.

- Name another pair of supplementary angles.

- If \begin{align*}m\angle INJ = 63^\circ\end{align*}, find \begin{align*}m\angle JNL\end{align*}.

For exercises 10-13, determine if the statement is true or false.

- Supplementary angles add up to \begin{align*}180^\circ\end{align*}.
- Two angles on a straight line are supplementary angles.
- To be supplementary, two angles must be touching.
- It's possible for two angles in a triangle to be supplementary.

For 14-15, find the value of \begin{align*}x\end{align*}.