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LESSON
Name
Date
13.2 Study Guide
For use with pages 716–720
GOAL
Identify angles when a transversal intersects lines.
VOCABULARY
A line that intersects two or more lines at different points is a
transversal. When a transversal intersects two lines, several pairs of
angles are formed. Two angles that occupy corresponding positions
are corresponding angles. Two angles that lie between the two lines
on opposite sides of the transversal are alternate interior angles.
Two angles that lie outside the two lines on opposite sides of the
transversal are alternate exterior angles.
EXAMPLE
1 Identifying Angles
t
In the diagram, line t is a transversal. Tell whether the
angles are corresponding, alternate interior, or alternate
exterior angles.
b. a3 and a6
c. a2 and a7
Solution
a. a4 and a8 are corresponding angles.
b. a3 and a6 are alternate interior angles.
c. a2 and a7 are alternate exterior angles.
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6
7
q
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Exercises for Example 1
In Example 1, tell whether the angles are corresponding, alternate interior, or
alternate exterior angles.
1. a1 and a5
EXAMPLE
2. a4 and a5
3. a1 and a8
2 Finding Angle Measures
In the diagram, transversal t intersects parallel lines
l and m. If ma1 ⫽ 125⬚, find the measures of the
other numbered angles.
m
2
Solution
ma5 ⫽ 125⬚, because a1 and a5 are corresponding angles.
ma4 ⫽ 125⬚, because a4 and a5 are alternate interior angles.
ma8 ⫽ 125⬚, because a1 and a8 are alternate exterior angles.
ma2 ⫽ 55⬚, because a1 and a2 are supplementary angles.
ma6 ⫽ 55⬚, because a2 and a6 are corresponding angles.
ma3 ⫽ 55⬚, because a3 and a6 are alternate interior angles.
ma7 ⫽ 55⬚, because a2 and a7 are alternate exterior angles.
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Chapter 13
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Pre-Algebra
Resource Book
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Lesson 13.2
a. a4 and a8
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LESSON
Name
Date
13.2 Study Guide
Continued
For use with pages 716–720
Exercises for Example 2
Find the measures of the numbered angles in the diagram.
4.
5.
154⬚
1
82⬚
3
2
5
4
6
7
4
7
2
5
1
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EXAMPLE
3 Finding the Value of a Variable
Find the value of x that makes lines m and n parallel
given that ma2 ⫽ (3x ⫹ 14)⬚ and ma8 ⫽ 115⬚.
t
1
Lesson 13.2
Solution
a2 and a6 are corresponding angles and a6 and a8
are supplementary. Lines m and n are parallel when
ma2 ⫽ ma6.
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5
7
2
4
6
8
m
(1) Find ma6.
ma6 ⫹ ma8 ⫽ 180⬚
ma6 ⫹ 115⬚ ⫽ 180⬚
ma6 ⫽ 65⬚
a6 and a8 are supplementary.
Substitute 115⬚ for ma8.
Subtract 115⬚ from each side.
n
(2) Find x.
ma2 ⫽ ma6
(3x ⫹ 14)⬚ ⫽ 65⬚
3x ⫽ 51
x ⫽ 17
Set measures equal.
Substitute (3x ⫹ 14)⬚ for ma2 and 65⬚ for ma6.
Subtract 14 from each side.
Divide each side by 3.
Answer: When x ⫽ 17, lines m and n are parallel.
Exercise for Example 3
Find the value of x that makes lines p and q parallel.
6.
t
(2x ⫹ 1)⬚
p
95⬚
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Pre-Algebra
Chapter 13 Resource Book
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Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.