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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.

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CK-12 Foundation: Chapter1Linear PairsA

James Sousa: Linear Pairs


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.

CK-12 Foundation: Chapter1LinearPairsB

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

Interactive Practice

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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.

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 .

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