716 Chapter 9 An Introduction to Geometry
Self Check 1
Classify , , , and
in the figure as an acute
angle, a right angle, an obtuse
angle, or a straight angle.GED
EFGDEF 1
EXAMPLE (^1) Classify each angle in the figure as
an acute angle, a right angle, an obtuse angle, or a straight
angle.
StrategyWe will determine how each angle’s measure
compares to 90° or to 180°.
A
B
D
E
C
1
2
WHYAcute, right, obtuse, and straight angles are defined
with respect to 90° and 180° angle measures.
Solution
Since , it is an acute angle.
Since but less than 180°, it is an obtuse angle.
Since , it is a right angle.
Since m(ABC)180°, it is a straight angle.
m(BDE)90°
m(2)90°
Now TryProblems 57, 59, and 61 m(1)90°
D E
F
G
1
5 Solve problems involving adjacent angles.
Two angles that have a common vertex and a common side are called adjacent angles
if they are side-by-side and their interiors do not overlap.
Success Tip We can use the algebra concepts of variable and equation that
were introduced in Chapter 8 to solve many types of geometry problems.
EXAMPLE (^2) Two angles with degree measures
of xand 35° are adjacent angles, as shown. Use the
information in the figure to find x.
StrategyWe will write an equation involving xthat
mathematically models the situation.
WHYWe can then solve the equation to find the
unknown angle measure.
Solution
Since the sum of the measures of the two adjacent angles is 80°, we have
The word sumindicates addition.
To isolate x,undo the addition of 35° by
subtracting 35° from both sides.
Do the subtractions: 35°35°0°
and 80°35°45°.
Thus,xis 45°. As a check, we see that 45°35°80°.
x45°
x35° 35 80° 35
x35°80°
Self Check 2
Use the information in the figure
to find x.
Now TryProblem 65
125°
160°
x
80°
35°
Adjacent angles
x
6 Use the property of vertical angles to solve problems.
When two lines intersect, pairs of nonadjacent angles are called vertical angles.In the
following figure, 1 and 3 are vertical angles and 2 and 4 are vertical angles.
Caution! In the figure for Example 2, we used the variable xto represent an
unknown angle measure. In such cases, we will assume that the variable
“carries” with it the associated units of degrees. That means we do not have to
write a ° symbol next to the variable. Furthermore, if xrepresents an unknown
number of degrees, then expressions such as , , and also
have units of degrees.
3 xx15° 4 x20°
8
7
0
10
35
45