Supplementary Angles
Bill Zahner
Lori Jordan
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Printed: March 7, 2016
AUTHORS
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Supplementary Angles
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Supplementary Angles
Here you’ll learn what supplementary angles are and how they can help you to solve problems.
What if you were given two supplementary angles? How would you determine their angle measures? After
completing this Concept, you’ll be able to use the definition of supplementary angles to solve problems like this
one.
Watch This
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/136963
CK-12 Foundation: Chapter1SupplementaryAnglesA
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/1274
James Sousa: Supplementary Angles
Guidance
Two angles are supplementary when they add up to 180◦ . Supplementary angles do not have to be congruent or
touching.
Example A
The two angles below are supplementary. If m6 MNO = 78◦ what is m6 PQR?
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Set up an equation.
78◦ + m6 PQR = 180◦
m6 PQR = 102◦
Example B
What are the measures of two congruent, supplementary angles?
Supplementary angles add up to 180◦ . Congruent angles have the same measure. Divide 180◦ by 2, to find the
measure of each angle.
180◦ ÷ 2 = 90◦
So, two congruent, supplementary angles are right angles, or 90◦ .
Example C
Name one pair of supplementary angles in the diagram below.
One example is 6 INM and 6 MNL.
Watch this video for help with the Examples above.
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/136964
CK-12 Foundation: Chapter1SupplementaryAnglesB
Guided Practice
Find the measure of an angle that is supplementary to 6 ABC if m6 ABC is
1. 45◦
2. 118◦
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Chapter 1. Supplementary Angles
3. 32◦
4. x◦
Answers:
1. 135◦
2. 62◦
3. 148◦
4. 180 − x◦
Interactive Practice
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/113041
Explore More
Find the measure of an angle that is supplementary to 6 ABC if m6 ABC is:
1.
2.
3.
4.
5.
6.
7.
112◦
15◦
97◦
81◦
57◦
(x − y)◦
(x + y)◦
←
→
Use the diagram below for exercises 8-9. Note that NK ⊥ IL .
8. Name another pair of supplementary angles.
9. If m6 INJ = 63◦ , find m6 JNL.
For exercises 10-13, determine if the statement is true or false.
10. Supplementary angles add up to 180◦ .
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11. Two angles on a straight line are supplementary angles.
12. To be supplementary, two angles must be touching.
13. It’s possible for two angles in a triangle to be supplementary.
For 14-15, find the value of x.
14.
15.
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 1.8.
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