Page 648 - Basic College Mathematics with Early Integers

S E C T ION 9 .1 I LINES AND ANGLES 625

Example 5 Find the supplement of a 107° angle. PRACTICE 5

Find the supplement of a 67°
Solution: Two angles that have a sum of 180° are supplementary. This means angle.
that the supplement of an angle that measures 107° is an angle that measures
180° - 107° = 73°.
Work Practice 5

Concept Check True or false? The supplement of a 48° angle is 42°.
Explain.

Objective Finding Measures of Angles

Measures of angles can be added or subtracted to find measures of related angles.

Example 6 Find the measure of ∠x. Then classify ∠x as an acute, obtuse, or PRACTICE 6
right angle.
a. Find the measure of ∠y.
Solution: m∠x = m∠QTS - m∠RTS
= 87° - 52° Q B
R
= 35° 141
A
y 97
Thus, the measure of ∠x (m∠x) is 35°. x 52 87
Since ∠x measures between 0° and 90°, D C
T
it is an acute angle. S
b. Find the measure of ∠x.
Work Practice 6

Two lines in a plane can be either parallel or intersecting.Parallel lines never meet.
Intersecting lines meet at a point. The symbol is used to indicate “is parallel to.” For
7
79 x
example, in the figure, p 7 q. 51
p l
T
c. Classify ∠x and ∠y as
q acute, obtuse, or right angles.
k
Parallel lines Intersecting lines
Some intersecting lines are perpendicular. Two lines are perpendicular if they
form right angles when they intersect. The symbol is used to denote “is perpen-
dicular to.” For example, in the figure below, m n.

m

n

Perpendicular lines

When two lines intersect, four angles
Vertical angles:
are formed. Two angles that are opposite a and c
each other are called vertical angles. d and b Answers
Vertical angles have the same measure. a 5. 113° 6. a. 44° b. 28° c. acute
Two angles that share a common side d c b Adjacent angles:
are called adjacent angles. Adjacent angles a and b
b and c Concept Check Answer
formed by intersecting lines are supplemen- c and d false; the complement of a 48° angle is
tary.That is,the sum of their measures is 180°. d and a 42°; the supplement of a 48° angle is 132°