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Linear Pairs
Dan Greenberg
Andrew Gloag
Jim Sconyers
Bill Zahner
Lori Jordan
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Printed: July 10, 2016
AUTHORS
Dan Greenberg
Andrew Gloag
Jim Sconyers
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Linear Pairs
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Linear Pairs
Here you’ll learn what linear pairs are and how to solve linear pair problems.
Linear Pairs
Two angles are adjacent if they have the same vertex, share a side, and do not overlap. 6 PSQ and 6 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◦ ). 6 PSQ and 6 QSR are a linear pair.
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?
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/136737
Examples
←
→
For Examples 1 and 2, use the diagram below. Note that NK ⊥ IL .
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Example 1
Name one linear pair of angles.
6
MNLand 6 LNJ
Example 2
What is m6 INL?
180◦
Example 3
What is the measure of each angle?
These two angles are a linear pair, so they add up to 180◦ .
(7q − 46)◦ + (3q + 6)◦ = 180◦
10q − 40◦ = 180◦
10q = 220◦
q = 22◦
Plug in q to get the measure of each angle. m6 ABD = 7(22◦ ) − 46◦ = 108◦ m6 DBC = 180◦ − 108◦ = 72◦
Example 4
Are 6 CDA and 6 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◦ : 120◦ + 60◦ = 180◦ .
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Chapter 1. Linear Pairs
Example 5
Find the measure of an angle that forms a linear pair with 6 MRS if m6 MRS is 150◦ .
Because linear pairs have to add up to 180◦ , the other angle must be 180◦ − 150◦ = 30◦ .
Review
For 1-5, determine if the statement is true or false.
1.
2.
3.
4.
5.
Linear pairs are congruent.
Adjacent angles share a vertex.
Adjacent angles overlap.
Linear pairs are supplementary.
Supplementary angles form linear pairs.
For exercise 6, find the value of x.
6.
Find the measure of an angle that forms a linear pair with 6 MRS if m6 MRS is:
7.
8.
9.
10.
11.
12.
61◦
23◦
114◦
7◦
179◦
z◦
Review (Answers)
To see the Review answers, open this PDF file and look for section 1.9.
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