Download Study guide

Name———————————————————————— Lesson
1.5
Date —————————————
Study Guide
For use with the lesson “Describe Angle Pair Relationships”
goal
Use special angle relationships to find angle measures.
Vocabulary
Two angles are complementary if the sum of their measures is 908.
Two angles are supplementary if the sum of their measures is 1808.
Adjacent angles are two angles that share a common vertex and side,
but have no common interior points.
Two adjacent angles are a linear pair if their noncommon sides are
opposite rays.
Two angles are vertical angles if their sides form two pairs of
opposite rays.
Identify complements and supplements
In the figure, name a pair of complementary angles, a pair
of supplementary angles, and
a pair of adjacent angles.
D
A
308
C
O
1208
608
M
N
B
Solution
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Lesson 1.5
example 1
Because 608 1 308 5 908, ∠ ABD and ∠ DBC are complementary angles.
Because 608 1 1208 5 1808, ∠ ABD and ∠ MNO are supplementary angles.
Because ∠ ABD and ∠ DBC share a common vertex and side, they are adjacent angles.
Exercise for Example 1
1. In the figure, name a pair of complementary angles, a pair
of supplementary angles, and
a pair of adjacent angles.
example 2
D
O
C
1108
A
708
208
M
B
N
Find measures of a complement and a supplement
a. Given that ∠ 1 is a complement of ∠ 2 and m∠ 1 5 508, find m∠ 2.
b. Given that ∠ 3 is a supplement of ∠ 4 and m∠ 3 5 1058, find m∠ 4.
Solution
a. You can draw a diagram with complementary adjacent angles to illustrate the relationship.
m∠ 2 5 908 2 m∠ 1 5 908 2 508 5 408
b. You can draw a diagram with supplementary adjacent angles to illustrate the relationship.
m∠ 4 5 1808 2 m∠ 3 5 1808 2 1058 5 758
1
508
2
1058
3 4
Geometry
Chapter Resource Book
CS10_CC_G_MECR710761_C1L05SG.indd 69
1-69
4/27/11 2:32:53 PM
Name———————————————————————— Lesson
1.5
Date —————————————
Study Guide continued
For use with the lesson “Describe Angle Pair Relationships”
Exercises for Example 2
2. Given that ∠ 1 is a complement of ∠ 2 and m∠ 1 5 558, find m∠ 2.
3. Given that ∠ 3 is a supplement of ∠ 4 and m∠ 3 5 808, find m∠ 4.
example 3
Identify angle pairs
Identify all of the linear pairs and all of the vertical angles in the figure at the right.
1
Solution
Lesson 1.5
3
4
To find linear pairs, look for adjacent angles whose
noncommon sides are opposite rays.
2
∠ 1 and ∠ 2 are a linear pair. ∠ 2 and ∠ 3 are also a linear pair. ∠ 3 and ∠ 4 are also
a linear pair. ∠ 1 and ∠ 4 are also a linear pair.
To find vertical angles, look for angles formed by intersecting lines.
∠ 1 and ∠ 3 are vertical angles. ∠ 2 and ∠ 4 are also vertical angles.
Find angle measures in a linear pair
Solve for x in the diagram at the right. Then find the measure of each angle.
Solution
2x 8 x 8
The two angles form a linear pair. Use the fact that
the angles of a linear pair are supplementary to write an equation.
x8 1 2x8 5 1808
Write an equation.
3x 5 180
Combine like terms.
x 5 60
Divide each side by 3.
The measures of the angles are 608 and 2(608) 5 1208.
Exercises for Examples 3 and 4
4. Identify all of the linear pairs and all of the
vertical angles in the figure at the right.
1
5
2
3
4
Solve for x in the diagram. Then find the measure of each angle.
5.
x8 x8
1-70
6.
4x 8 2x 8
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
example 4
7.
3x 8 x 8
Geometry
Chapter Resource Book
CS10_CC_G_MECR710761_C1L05SG.indd 70
4/27/11 2:32:53 PM