<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
You are viewing an older version of this Concept. Go to the latest version.

Linear Pairs

Two adjacent angles that form a straight line.

Atoms Practice
Estimated7 minsto complete
Practice Linear Pairs
Estimated7 minsto complete
Practice Now
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


Two angles are adjacent if they have the same vertex, share a side, and do not overlap \begin{align*}\angle PSQ\end{align*}PSQ and \begin{align*}\angle QSR\end{align*}QSR 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 \begin{align*}180^\circ\end{align*}180). \begin{align*}\angle PSQ\end{align*}PSQ and \begin{align*}\angle QSR\end{align*}QSR 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 \begin{align*}180^\circ\end{align*}180.

\begin{align*}(7q-46)^\circ + (3q+6)^\circ &= 180^\circ\\ 10q - 40^\circ &= 180^\circ\\ 10q & = 220\\ q & = 22\end{align*}(7q46)+(3q+6)10q4010qq=180=180=220=22

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

Example B

Are \begin{align*}\angle CDA\end{align*}CDA and \begin{align*}\angle DAB\end{align*}DAB 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 \begin{align*}180^\circ\end{align*}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 \begin{align*}\angle MRS\end{align*} if \begin{align*} m\angle MRS\end{align*} is \begin{align*} 150^\circ\end{align*}.

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

CK-12 Linear Pairs

Guided Practice

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

1. Name one linear pair of angles.

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

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

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


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

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

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

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


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

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

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

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

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


Adjacent Angles

Adjacent Angles

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.


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

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Linear Pairs.
Please wait...
Please wait...

Original text