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# Linear Pairs

## Two adjacent angles that form a straight line.

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Practice Linear Pairs
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Linear Pairs

What if you notice two angles in a picture that make a straight line? What information does this give you about the angles? After completing this Concept, you'll be able to apply the properties of linear pairs to help you solve problems.

### Guidance

Adjacent angles are two angles that have the same vertex, share a side, and do not overlap. In the picture below, $\angle PSQ$ 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.

$\angle PSQ$ and $\angle QSR$ are a linear pair.

$m \angle PSR & = 180^\circ\\m \angle PSQ + m \angle QSR & = m \angle PSR\\m \angle PSQ + m \angle QSR & = 180^\circ$

#### Example A

What is the value of each angle?

These two angles are a linear pair, so they are supplementary, or add up to $180^\circ$ . Write an equation.

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

So, plug in $q$ to get the measure of each angle.

$m \angle ABD = 7(22^\circ) - 46^\circ = 108^\circ \quad m \angle DBC = 180^\circ - 108^\circ = 72^\circ$

#### 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. However, they are supplementary, $120^\circ + 60^\circ = 180^\circ$ .

#### Example C

Name one linear pair in the diagram below.

One example is $\angle INM$ and $\angle MNL$ .

Watch this video for help with the Examples above.

### Vocabulary

Adjacent angles are two angles that have the same vertex, share a side, and do not overlap. 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 .

### Guided Practice

1. What is $m\angle INL$ ?

2. What is $m\angle LNK$ ?

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

1. $180^\circ$

2. $90^\circ$

3. $180^\circ - 63^\circ=117^\circ$

### 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.

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

1. $54^\circ$
2. $32^\circ$
3. $104^\circ$
4. $71^\circ$
5. $149^\circ$
6. $x^\circ$

For 12-16, find the value of $x$ .

### Vocabulary Language: English

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

Diagram

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

linear pair

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