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Study Guide and Intervention
Angle Relationships
Pairs of Angles Adjacent angles are two angles that lie in the same plane and have a
common vertex and a common side, but no common interior points. A pair of adjacent angles
with noncommon sides that are opposite rays is called a linear pair. Vertical angles are
two nonadjacent angles formed by two intersecting lines.
Example
Name an angle or angle pair that satisfies each condition.
a. two vertical angles
$
∠EFI and ∠GFH are nonadjacent angles
formed by two intersecting lines. They are
vertical angles.
%
"
(
&
'
#
b. two adjacent angles
)
*
∠ABD and ∠DBE have a common vertex and
a common side but no common interior points.
They are adjacent angles.
c. two supplementary angles
∠EFG and ∠GFH form a linear pair. The angles are supplementary.
d. two complementary angles
Exercises
Name an angle or angle pair that satisfies each condition.
1. two adjacent angles
L
2. two acute vertical angles
3. two supplementary adjacent angles
N
110°
R
T
4. an angle supplementary to ∠RTS
E
S
For Exercises 5–7, use the figure at the right.
5. Identify two obtuse vertical angles.
S
R
V
6. Identify two acute adjacent angles.
N
U
7. Identify an angle supplementary to ∠TNU.
T
8. Find the measures of two complementary angles if the difference in their measures is 18.
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Lesson 1-5
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m∠CBD + m∠DBE = 90. These angles are complementary.
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Study Guide and Intervention
PERIOD
(continued)
Angle Relationships
Perpendicular Lines
Lines, rays, and segments that form four
right angles are perpendicular. The right angle symbol indicates that
!"# is perpendicular
the lines are perpendicular. In the figure at the right, AC
!"# ⊥ BD
!"#, or AC
!"#.
to BD
Example
A
B
C
D
" and ZP
" are perpendicular.
Find x so that DZ
""# ⊥ ZP
""#, then m∠DZP = 90.
If DZ
m∠DZQ + m∠QZP = m∠DZP
(9x + 5) + (3x + 1) = 90
12x + 6 = 90
12x = 84
x=7
D
Q
(9x + 5)°
(3x + 1)°
Sum of parts = whole
Substitution
Z
P
Combine like terms.
Subtract 6 from each side.
Divide each side by 12.
Exercises
!""#.
!""# ⊥ MQ
1. Find the value of x and y so that NR
2. Find m∠MSN.
N
P
5x°
M
x°
(9y + 18)° S
Q
""# ⊥ BF
""# . Find
3. m∠EBF = 3x + 10, m∠DBE = x, and BD
the value of x.
E
D
4. If m∠EBF = 7y - 3 and m∠FBC = 3y + 3, find the value of y
""#.
""# ⊥ BC
so that BE
F
B
A
C
5. Find the value of x, m∠PQS, and m∠SQR.
P
S
3x°
(8x + 2)°
Q
R
6. Find the value of y, m∠RPT, and m∠TPW.
T
(4y - 5)°
(2y + 5)°
R
P
W
V
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
R
S
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Skills Practice
Angle Relationships
For Exercises 1–6, use the figure at the right. Name an
angle or angle pair that satisfies each condition.
E
F
1. Name two acute vertical angles.
K
2. Name two obtuse vertical angles.
H
G
J
3. Name a linear pair.
4. Name two acute adjacent angles.
5. Name an angle complementary to ∠EKH.
6. Name an angle supplementary to ∠FKG.
7. Find the measures of an angle and its complement if one angle measures 24 degrees
more than the other.
8. The measure of the supplement of an angle is 36 less than the measure of the angle.
Find the measures of the angles.
R
""#.
""# ⊥ TS
9. If m∠RTS = 8x + 18, find the value of x so that TR
10. If m∠PTQ = 3y - 10 and m∠QTR = y, find the value of y
so that ∠PTR is a right angle.
Q
P
T
Determine whether each statement can be assumed
from the figure. Explain.
S
W
V
11. ∠WZU is a right angle.
X
Z
U
Y
12. ∠YZU and ∠UZV are supplementary.
13. ∠VZU is adjacent to ∠YZX.
Lesson 1-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ALGEBRA For Exercises 9–10, use the figure at the right.
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Practice
Angle Relationships
Name an angle or angle pair that satisfies each condition.
G
H
50°
F
1. Name two obtuse vertical angles.
C
B
2. Name a linear pair with vertex B.
50°
3. Name an angle not adjacent to, but complementary
to ∠FGC.
A
E
D
4. Name an angle adjacent and supplementary to ∠DCB.
5. ALGEBRA Two angles are complementary. The measure of one angle is 21 more than
twice the measure of the other angle. Find the measures of the angles.
6. ALGEBRA If a supplement of an angle has a measure 78 less than the measure of the
angle, what are the measures of the angles?
ALGEBRA For Exercises 7–8, use the figure at
A
the right.
7. If m∠FGE = 5x + 10, find the value of x so that
"#$ ⊥ AE
"#$.
FC
B
C
G
F
E
Determine whether each statement can be
assumed from the figure. Explain.
N
O
9. ∠NQO and ∠OQP are complementary.
P
Q
M
10. ∠SRQ and ∠QRP is a linear pair.
R
12. STREET MAPS Darren sketched a map of the cross streets
nearest to his home for his friend Miguel. Describe two
different angle relationships between the streets.
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Be
11. ∠MQN and ∠MQR are vertical angles.
aco
n
S
Olive
Ma
in
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
D
8. If m∠BGC = 16x - 4 and m∠CGD = 2x + 13,
find the value of x so that ∠BGD is a right angle.
Glencoe Geometry
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