Page 649 - Basic College Mathematics with Early Integers

626 C HAPTE R 9 I GEOMETRY

Here are a few real-life examples of the lines we just discussed.

Central Ave. 25th St. Beam Rd.
California St. 17th St.
Chestnut St. 10th St. McClure Rd.

7th St.

Parallel lines Vertical angles Perpendicular lines

PRACTICE 7 Example 7 Find the measures of ∠x, ∠y, and ∠z if the measure of ∠t is 42°.

Find the measures of ∠a, ∠b,
and ∠c. y
x t
z

Solution: Since ∠t and ∠x are vertical angles, they have the same measure, so
b
a 109 ∠x measures 42°.
c
Since ∠t and ∠y are adjacent angles, their measures have a sum of 180°. So ∠y
measures 180° - 42° = 138°.
Since ∠y and ∠z are vertical angles, they have the same measure. So ∠z
measures 138°.
Work Practice 7

A line that intersects two or more lines at different
points is called a transversal. Line l is a transversal that a b
m
intersects lines m and n. The eight angles formed have c d
special names. Some of these names are:
e f n
Corresponding angles: ∠a and ∠e, ∠c and ∠g, ∠b g h
and ∠f, ∠d and ∠h l
Alternate interior angles: ∠c and ∠f, ∠d and ∠e
When two lines cut by a transversal are parallel, the following statement is true:

PRACTICE 8
Parallel Lines Cut by a Transversal
Given that m 7 n and that the
measure of ∠w = 45°, find If two parallel lines are cut by a transversal, then the measures of corresponding
the measures of all the angles angles are equal and the measures of the alternate interior angles are equal.
shown.

w a m Example 8
b x Given that m 7 n and that the
measure of ∠w is 100°, find the x
y c measures of ∠x, ∠y, and ∠z. w m
n
z d
z y
n
Answers
Solution:
7. m∠a = 109°; m∠b = 71°;
m∠c = 71° m∠x = 100° ∠x and ∠w are vertical angles.
8. m∠x = 45°; m∠y = 45°; Copyright 2012 Pearson Education, Inc.
m∠z = 135°; m∠z = 100° ∠x and ∠z are corresponding angles.
m∠a = 135°; m∠y = 180° - 100° = 80° ∠z and ∠y are supplementary angles.
m∠b = 135°;
m∠c = 135°;
m∠d = 45° Work Practice 8