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Supplementary Angles

Two angles that add to 180 degrees.

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Supplementary Angles

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.

Guidance

Two angles are supplementary when they add up to 180\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 mMNO=78\begin{align*}m \angle MNO = 78^\circ\end{align*} what is mPQR\begin{align*}m \angle PQR\end{align*}?

Set up an equation.

78+mPQR=180mPQR=102

Example B

What are the measures of two congruent, supplementary angles?

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

180÷2=90

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

Example C

Name one pair of supplementary angles in the diagram below.

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

Watch this video for help with the Examples above.

Vocabulary

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

Guided Practice

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

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

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

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

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

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

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

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

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

Practice

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

1. 112\begin{align*}112^\circ\end{align*}
2. 15\begin{align*}15^\circ\end{align*}
3. 97\begin{align*}97^\circ\end{align*}
4. 81\begin{align*}81^\circ\end{align*}
5. 57\begin{align*}57^\circ\end{align*}
6. (xy)\begin{align*}(x-y)^\circ\end{align*}
7. (x+y)\begin{align*}(x+y)^\circ\end{align*}

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

1. Name another pair of supplementary angles.
1. If mINJ=63\begin{align*}m\angle INJ = 63^\circ\end{align*}, find mJNL\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 180\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 x\begin{align*}x\end{align*}.

Vocabulary Language: English

Supplementary angles

Supplementary angles

Supplementary angles are two angles whose sum is 180 degrees.