Download 1.20 Complementary Angles

1.20. Complementary Angles
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1.20 Complementary Angles
Here you’ll learn what complementary angles are and how to solve complementary angle problems.
What if you were given two angles of unknown size and were told they are complementary? How would you
determine their angle measures? After completing this Concept, you’ll be able to use the definition of complementary
angles to solve problems like this one.
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CK-12 Complementary Angles
Watch this video beginning at around the 3:20 mark.
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James Sousa:Angle Basics–ComplementaryAngles
Then watch the first part of this video.
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James Sousa:Complementary Angles
Guidance
Two angles are complementary if they add up to 90◦ . Complementary angles do not have to be congruent or next
to each other.
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
Example A
The two angles below are complementary. m GHI = x. What is x?
Because the two angles are complementary, they add up to 90◦ . Make an equation.
x + 34◦ = 90◦
x = 56◦
Example B
The two angles below are complementary. Find the measure of each angle.
The two angles add up to 90◦ . Make an equation.
(8r + 9) + (7r + 6) = 90
(15r + 15) = 90
15r = 75
r=5
However, you need to find each angle. Plug r back into each expression.
m GHI = 8(5◦ ) + 9◦ = 49◦
m JKL = 7(5◦ ) + 6◦ = 41◦
Example C
Find the measure of an angle that is complementary to MRS if m MRS is 70◦ .
Because complementary angles have to add up to 90◦ , the other angle must be 90◦ − 70◦ = 20◦ .
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1.20. Complementary Angles
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CK-12 Complementary Angles
Guided Practice
Find the measure of an angle that is complementary to ABC if m ABC is:
1.
2.
3.
4.
45◦
82◦
19◦
12◦
Answers:
1. Because complementary angles have to add up to 90◦ , the other angle must be 90◦ − 45◦ = 45◦ .
2. Because complementary angles have to add up to 90◦ , the other angle must be 90◦ − 82◦ = 8◦ .
3. Because complementary angles have to add up to 90◦ , the other angle must be 90◦ − 19◦ = 71◦ .
4. Because complementary angles have to add up to 90◦ , the other angle must be 90◦ − 12◦ = 78◦ .
Practice
Find the measure of an angle that is complementary to ABC if m ABC is:
1.
2.
3.
4.
5.
6.
7.
4◦
89◦
54◦
32◦
27◦
(x + y)◦
z◦
←
→
Use the diagram below for exercises 8-9. Note that NK ⊥ IL .
8. Name two complementary angles.
9. If m INJ = 63◦ , find m KNJ.
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
For 10-11, determine if the statement is true or false.
10. Complementary angles add up to 180◦ .
11. Complementary angles are always 45◦ .
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