Download 1.6 Practice with Examples

MCRBG-0106-PE.qxd
3-16-2001
2:25 PM
Page 16
LESSON
1.6
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 44–50
GOAL
Identify vertical angles and linear pairs and identify complementary and
supplementary angles
VOCABULARY
Two angles are vertical angles if their sides form two pairs of opposite
rays.
Chapter 1
Two adjacent angles are a linear pair if their noncommon sides are
opposite rays.
Two angles are complementary angles if the sum of their measures is
90 . Each angle is the complement of the other.
Two angles are supplementary angles if the sum of their measures is
180 . Each angle is the supplement of the other.
EXAMPLE 1
Identifying Vertical Angles and Linear Pairs
a. Are 1 and 3 vertical angles?
b. Are 2 and 4 a linear pair?
c. Are 1 and 4 a linear pair?
1
4
2
3
SOLUTION
a. Yes. The sides of the angles form two pairs
of opposite rays.
b. No. The angles are not adjacent.
c. Yes. The angles are adjacent and their noncommon sides are opposite rays.
16
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
MCRBG-0106-PE.qxd
3-16-2001
2:25 PM
LESSON
1.6
CONTINUED
Page 17
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 44–50
Exercises for Example 1
Use the figure to answer the questions.
1.
2.
4
3
1
2 3
5 4
a. Are 1 and 2 a linear pair?
a. Are 1 and 5 a linear pair?
b. Are 1 and 3 vertical angles?
b. Are 1 and 2 a linear pair?
c. Are 1 and 4 a linear pair?
c. Are 1 and 4 vertical angles?
d. Are 2 and 4 vertical angles?
d. Are 3 and 5 vertical angles?
Finding Angle Measures
Solve for x in the diagram at the right.
Then find the angle measures.
SOLUTION
Use the fact that vertical angles are congruent.
7x 25 5x 15
x 20
F
G
(7x 25) H
(5x 15)
I
J
Use substitution to find the angle measures.
20 25 115
mGHJ 5x 15 5 20 15 115
mFHI 7x 25 7
Next, realize that FHI and FHG are a linear pair. So, the measures of these
two angles must sum to 180. So, mFHG 180 115, so mFHG 65.
Finally, notice that FHG and IHJ are vertical angles. So, mIHJ 65.
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
17
Chapter 1
EXAMPLE 2
1
2
MCRBG-0106-PE.qxd
3-16-2001
LESSON
1.6
CONTINUED
2:25 PM
Page 18
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 44–50
Exercises for Example 2
Solve for x and y, then find the angle measures.
3.
4.
B
G
(5y 50)
F
A
6x E
C
J
(4y 10)
Chapter 1
(3x 45)
H
I
D
EXAMPLE 3
Finding Measures of Complements and Supplements
a. Given that E is a complement of F and mE 68, find mF.
b. Given that G is a supplement of H and mG 152, find mH.
SOLUTION
a. mF 90 mE 90 68 22
b. mH 180 mG 180 152 28
Exercises for Example 3
Find the measure of the angle.
5. Given that A is a complement of B and mB 81, find mA.
6. Given that C is a supplement of D and mC 27, find mD.
18
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.