<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Linear Pairs

## Two adjacent angles that form a straight line.

0%
Progress
Practice Linear Pairs
Progress
0%
Linear Pairs

What if you were given two angles of unknown size and were told they form a linear pair? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of linear pair to solve problems like this one.

### Watch This

CK-12 Linear Pairs

### Guidance

Two angles are adjacent if they have the same vertex, share a side, and do not overlap PSQ\begin{align*}\angle PSQ\end{align*} and QSR\begin{align*}\angle QSR\end{align*} are adjacent.

A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary (add up to 180\begin{align*}180^\circ\end{align*}). PSQ\begin{align*}\angle PSQ\end{align*} and QSR\begin{align*}\angle QSR\end{align*} are a linear pair.

#### Example A

What is the measure of each angle?

These two angles are a linear pair, so they add up to 180\begin{align*}180^\circ\end{align*}.

(7q46)+(3q+6)10q4010qq=180=180=220=22

Plug in q\begin{align*}q\end{align*} to get the measure of each angle. mABD=7(22)46=108 mDBC=180108=72\begin{align*}m\angle ABD = 7(22^\circ) - 46^\circ = 108^\circ \ m\angle DBC = 180^\circ - 108^\circ = 72^\circ\end{align*}

#### Example B

Are CDA\begin{align*}\angle CDA\end{align*} and DAB\begin{align*}\angle DAB\end{align*} a linear pair? Are they supplementary?

The two angles are not a linear pair because they do not have the same vertex. They are supplementary because they add up to 180\begin{align*}180^\circ\end{align*}: 120+60=180\begin{align*}120^\circ + 60^\circ = 180^\circ\end{align*}.

#### Example C

Find the measure of an angle that forms a linear pair with MRS\begin{align*}\angle MRS\end{align*} if mMRS\begin{align*} m\angle MRS\end{align*} is 150\begin{align*} 150^\circ\end{align*}.

Because linear pairs have to add up to 180\begin{align*}180^\circ\end{align*}, the other angle must be 180150=30\begin{align*}180^\circ-150^\circ=30^\circ\end{align*}.

CK-12 Linear Pairs

-->

### Guided Practice

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

1. Name one linear pair of angles.

2. What is mINL\begin{align*}m\angle INL\end{align*}?

3. What is mLNK\begin{align*}m\angle LNK\end{align*}?

4. If mINJ=63\begin{align*}m\angle INJ = 63^\circ\end{align*}, find mMNI\begin{align*}m\angle MNI\end{align*}.

1. MNL\begin{align*} \angle MNL \end{align*} and LNJ\begin{align*}\angle LNJ\end{align*}

2. 180\begin{align*}180^\circ\end{align*}

3. 90\begin{align*}90^\circ\end{align*}

4. 18063=117\begin{align*}180^\circ - 63^\circ=117^\circ\end{align*}

### Explore More

For 1-5, determine if the statement is true or false.

1. Linear pairs are congruent.
2. Adjacent angles share a vertex.
4. Linear pairs are supplementary.
5. Supplementary angles form linear pairs.

For exercise 6, find the value of x\begin{align*}x\end{align*}.

Find the measure of an angle that forms a linear pair with MRS\begin{align*}\angle MRS\end{align*} if mMRS\begin{align*} m\angle MRS\end{align*} is:

1. 61\begin{align*}61^\circ\end{align*}
2. 23\begin{align*}23^\circ\end{align*}
3. 114\begin{align*}114^\circ\end{align*}
4. 7\begin{align*}7^\circ\end{align*}
5. 179\begin{align*}179^\circ\end{align*}
6. z\begin{align*}z^\circ\end{align*}

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 1.9.

### Vocabulary Language: English Spanish

Two angles are adjacent if they share a side and vertex. The word 'adjacent' means 'beside' or 'next-to'.
linear pair

linear pair

Two angles form a linear pair if they are supplementary and adjacent.
Diagram

Diagram

A diagram is a drawing used to represent a mathematical problem.