# Supplementary Angles

## Two angles that add to 180 degrees.

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Supplementary Angles

### Supplementary Angles

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.

#### Measuring Supplementary Angles

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*}

#### Measuring Congruent, Supplementary Angles

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*}.

#### Identifying Supplementary Angles

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*}.

### Examples

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

#### Example 1

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

=\begin{align*}135^\circ\end{align*}

#### Example 2

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

=\begin{align*}62^\circ\end{align*}

#### Example 3

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

=\begin{align*}148^\circ\end{align*}

#### Example 4

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

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

### Review

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*}112^\circ\end{align*}
2. \begin{align*}15^\circ\end{align*}
3. \begin{align*}97^\circ\end{align*}
4. \begin{align*}81^\circ\end{align*}
5. \begin{align*}57^\circ\end{align*}
6. \begin{align*}(x-y)^\circ\end{align*}
7. \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*}.

1. Name a pair of supplementary angles.
1. 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.

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

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

To view the Review answers, open this PDF file and look for section 1.8.

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