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# Linear Pairs

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Practice Linear Pairs
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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.

### Guidance

Two angles are adjacent if they have the same vertex, share a side, and do not overlap $\angle PSQ$ and $\angle QSR$ 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 $180^\circ$ ). $\angle PSQ$ and $\angle QSR$ 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 $180^\circ$ .

$(7q-46)^\circ + (3q+6)^\circ &= 180^\circ\\10q - 40^\circ &= 180^\circ\\10q & = 220\\q & = 22$

Plug in $q$ to get the measure of each angle. $m\angle ABD = 7(22^\circ) - 46^\circ = 108^\circ \ m\angle DBC = 180^\circ - 108^\circ = 72^\circ$

#### Example B

Are $\angle CDA$ and $\angle DAB$ 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 $180^\circ$ : $120^\circ + 60^\circ = 180^\circ$ .

#### Example C

Find the measure of an angle that forms a linear pair with $\angle MRS$ if $m\angle MRS$ is $150^\circ$ .

Because linear pairs have to add up to $180^\circ$ , the other angle must be $180^\circ-150^\circ=30^\circ$ .

### Guided Practice

Use the diagram below. Note that $\overline{NK} \perp \overleftrightarrow{IL}$ .

1. Name one linear pair of angles.

2. What is $m\angle INL$ ?

3. What is $m\angle LNK$ ?

4. If $m\angle INJ = 63^\circ$ , find $m\angle MNI$ .

1. $\angle MNL$ and $\angle LNJ$

2. $180^\circ$

3. $90^\circ$

4. $180^\circ - 63^\circ=117^\circ$

### Practice

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 $x$ .

Find the measure of an angle that forms a linear pair with $\angle MRS$ if $m\angle MRS$ is:

1. $61^\circ$
2. $23^\circ$
3. $114^\circ$
4. $7^\circ$
5. $179^\circ$
6. $z^\circ$

### Vocabulary Language: English Spanish

Two angles are adjacent if they have the same vertex, share a side, and do not overlap.
linear pair

linear pair

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 $180^\circ$).