EXAMPLE 1 Identify complements and supplements In the figure, name a pair of complementary and angles, a pair of supplementary angles, and a pair of adjacent angles. non 122 58
EXAMPLE 1 Identify complements and supplements In the figure, name a pair of complementary and angles, a pair of supplementary angles, and a pair of adjacent angles. non 122 58
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.1: Angle Relationships
Problem 24E
Related questions
Topic Video
Question
Can you help me with problems 1 AND 2
![1.5 Describe Angle Pair
Relationships
Before
You used angle postulates to measure and classify angles.
Now
You will use special angle relationships to find angle measures.
Why?
So you can find measures in a building, as in Ex. 53.
Key Vocabulary
• complementary
angles
• supplementary
angles
• adjacent angles
• linear pair
• vertical angles
Two angles are complementary angles if the sum of their measures is 90°.
Each angle is the complement of the other. Two angles are supplementary
angles if the sum of their measures is 180°. Each angle is the supplement of
the other.
Complementary angles and supplementary angles can be adjacent angles
or nonadjacent angles. Adjacent angles are two angles that share a common
vertex and side, but have no common interior points.
Complementary angles
Supplementary angles
соммон
CORE
CC.9-12.G.CO.1 Know precise
definitions of angle, circle,
perpendicular line, parallel line,
and line segment, based on
the undefined notions of point,
line, distance along a line, and
distance around a circular arc.
Adjacent
Nonadjacent
Adjacent
Nonadjacent
EXAMPLE 1
Identify complements and supplements
In the figure, name a pair of complementary
angles, a pair of supplementary angles, and
a pair of adjacent angles.
AVOID ERRORS
****.........................*
In Example 1, Z DAC and
ZDAB share a common
vertex. But they share
common interior points,
so they are not adjacent
I 122
32
Solution
Because 32° + 58° = 90°, Z BAC and ZRST are complementary angles.
Because 122° + 58° = 180°, Z CAD and ZRST are supplementary angles.
angles.
Because ZBACand ZCAD share a common vertex and side, they are adjacent.
GUIDED PRACTICE
for Example 1
1. In the figure, name a pair of complementary
angles, a pair of supplementary
pair of adjacent angles.
G
gles, and a
41/131°
49
2. Are ZKGH and ZLKG adjacent angles? Are
ZFGK and ZFGH adjacent angles? Explain.
1.5 Describe Angle Pair Relationships
35](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5f48fcd-c459-4f35-9a71-35307def97f8%2F4672d7b7-e6f5-4651-86b9-c0b69f5851e0%2Fe4y9z3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.5 Describe Angle Pair
Relationships
Before
You used angle postulates to measure and classify angles.
Now
You will use special angle relationships to find angle measures.
Why?
So you can find measures in a building, as in Ex. 53.
Key Vocabulary
• complementary
angles
• supplementary
angles
• adjacent angles
• linear pair
• vertical angles
Two angles are complementary angles if the sum of their measures is 90°.
Each angle is the complement of the other. Two angles are supplementary
angles if the sum of their measures is 180°. Each angle is the supplement of
the other.
Complementary angles and supplementary angles can be adjacent angles
or nonadjacent angles. Adjacent angles are two angles that share a common
vertex and side, but have no common interior points.
Complementary angles
Supplementary angles
соммон
CORE
CC.9-12.G.CO.1 Know precise
definitions of angle, circle,
perpendicular line, parallel line,
and line segment, based on
the undefined notions of point,
line, distance along a line, and
distance around a circular arc.
Adjacent
Nonadjacent
Adjacent
Nonadjacent
EXAMPLE 1
Identify complements and supplements
In the figure, name a pair of complementary
angles, a pair of supplementary angles, and
a pair of adjacent angles.
AVOID ERRORS
****.........................*
In Example 1, Z DAC and
ZDAB share a common
vertex. But they share
common interior points,
so they are not adjacent
I 122
32
Solution
Because 32° + 58° = 90°, Z BAC and ZRST are complementary angles.
Because 122° + 58° = 180°, Z CAD and ZRST are supplementary angles.
angles.
Because ZBACand ZCAD share a common vertex and side, they are adjacent.
GUIDED PRACTICE
for Example 1
1. In the figure, name a pair of complementary
angles, a pair of supplementary
pair of adjacent angles.
G
gles, and a
41/131°
49
2. Are ZKGH and ZLKG adjacent angles? Are
ZFGK and ZFGH adjacent angles? Explain.
1.5 Describe Angle Pair Relationships
35
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