Download Angles

3-1
NAME ______________________________________DATE __________PERIOD______
Practice
Student Edition
Pages 90–94
Angles
Name each angle in four ways. Then identify its
vertex and its sides.
1.
2.
⬔LMN, ⬔NML, ⬔M,
and ⬔7
3.
⬔OPQ, ⬔QPO, ⬔P,
and ⬔8
⬔RST, ⬔TSR, ⬔S
and ⬔9
Name all angles having Q as their vertex.
4.
5.
⬔1, ⬔2, and ⬔UQW
6.
⬔3, ⬔4, ⬔XQZ
⬔5, ⬔6, ⬔7, ⬔AQC,
⬔BQD, and ⬔AQD
Tell whether each point is in the interior, exterior
or on the angle.
7.
8.
interior
10.
interior
9.
exterior
11.
on
12.
on
exterior
Tell whether each statement is true or false.
13. The vertex is in the exterior of the angle.
false
14. ⬔ABC, ⬔CBA, and ⬔B are all the same angle. true
15. Three rays are necessary to determine an angle. false
©
Glencoe/McGraw-Hill
T12
Geometry: Concepts and Applications
NAME ______________________________________DATE __________PERIOD______
3-2
Practice
Student Edition
Pages 96–101
Angle Measure
Use a protractor to find the measure of each angle.
Then classify each angle as acute, obtuse, or right.
1. ⬔JHI 40; acute
2. ⬔KHI 90; right
3. ⬔MHI 130; obtuse
4. ⬔LHI
110; obtuse
5. ⬔LHM
20; acute
6. ⬔LHK
20; acute
7. ⬔MHJ
90; right
8. ⬔MHK
40; acute
9. ⬔KHJ
50; acute
10. ⬔LHJ
70; acute
Use a protractor to draw an angle having each measurement.
Then classify each angle as acute, obtuse, or right. See student’s work.
11. 32° acute
12, 178° obtuse
13. 105° obtuse
14. 92° obtuse
15. 80° acute
16. 15° acute
17. 29° acute
18. 150° obtuse
19. 163° obtuse
20. 120° obtuse
©
Glencoe/McGraw-Hill
T13
Geometry: Concepts and Applications
3-3
NAME ______________________________________DATE __________PERIOD______
Practice
Student Edition
Pages 104–109
The Angle Addition Postulate
Refer to the figure at the right.
1. If m⬔BFC 35 and m⬔AFC 78
find m⬔1. 43
2. If m⬔BFC 20 and m⬔CFD 37
find m⬔BFD. 57
៮៬ bisects ⬔BFD, find ⬔CFD.
3. If m⬔BFD 60 and FC
30
4. If m⬔AFB 70 and m⬔BFC 15, find m⬔AFC.
85
5. If m⬔DFE 18 and m⬔CFE 45, find ⬔CFD.
27
Refer to the figure at the right.
6. If m⬔3 45 and m⬔JLI 20,
find m⬔ILK. 65
7. If m⬔GLJ 90, m⬔GLH 30, and
m⬔HLI 30, find m⬔ILJ. 30
8. If m⬔HLJ 70 and m⬔GLJ 90, find m⬔GLH. 20
9. If m⬔3 40 and m⬔JLH 60, find m⬔KLH. 100
10. If m⬔GLI 62 and m⬔GLH 40, find m⬔HLI. 22
11. If a right angle is bisected, what type of angles
are formed? acute
12. What type of angles are formed if a 40° angle
is bisected? acute
13. If m⬔1 30, m⬔2 3x, m⬔ABC 145, and
m⬔3 5x 5, find x. 15
©
Glencoe/McGraw-Hill
T14
Geometry: Concepts and Applications
3-4
NAME ______________________________________DATE __________PERIOD______
Practice
Student Edition
Pages 110–114
Adjacent Angles and Linear Pairs of Angles
Use the terms adjacent angles, linear pair, or neither
to describe angles 1 and 2 in as many ways as possible.
1.
2.
3.
adjacent angles;
linear pair
neither
neither
4.
5.
neither
6.
adjacent
angles;
linear pair
adjacent
៮៬ and GF
៮៬ are opposite
In the figure at the right GB
៮៬ and GD
៮៬ are opposite rays.
rays and GA
7. Which angle forms a linear pair with ⬔AGC?
⬔CGD
8. Do ⬔FGE and ⬔EGC form a linear pair? Justify your answer.
No; they do not contain sides that are opposite rays.
9. Name two angles that are adjacent angles.
Sample answer: ⬔DGE and ⬔EGF
10. Name three angles that are adjacent to ⬔EGD.
Sample answer: ⬔DGC, ⬔DGB, ⬔EGA
11. Which angle forms a linear pair with ⬔BGC?
⬔CGF
12. Name two adjacent angles that form a linear pair.
Sample answer: ⬔AGB and ⬔AGF
©
Glencoe/McGraw-Hill
T15
Geometry: Concepts and Applications
3-5
NAME ______________________________________DATE __________PERIOD______
Practice
Student Edition
Pages 116–121
Complementary and Supplementary Angles
Refer to the figures at the right.
1. Name an angle supplementary
to ⬔CBD. ⬔DBE
2. Name a pair of adjacent
supplementary angles.
Sample answer: ⬔CBA, ⬔ABE
Exercises 1–3
3. Name an angle complementary
to ⬔CBF. ⬔FBG
4. Name two angles that are complementary.
Sample answer: ⬔XQZ, ⬔ZQS
5. Find the measure of an angle that is
supplementary to ⬔XQZ. 140
6. Find the measure of the complement
of ⬔VQY. 50
Exercises 4–7
7. Name two angles that are supplementary.
Sample answer ⬔ZQX, ⬔XQV
8. Name an angle complementary to ⬔MON. ⬔MOL
9. Name an angle supplementary to ⬔POQ. ⬔POL
10. Find the measure of ⬔NOP. 70
Exercises 8–10
©
Glencoe/McGraw-Hill
T16
Geometry: Concepts and Applications
3-6
NAME ______________________________________DATE __________PERIOD______
Practice
Student Edition
Pages 122–127
Congruent Angles
Find the value of x in each figure.
1.
2.
55
4.
3.
110
47
5.
6.
52
43
25
7. What is the measure of an angle that is
supplementary to ⬔HIJ if ⬔HIJ ⬵ ⬔KLM? 126
8. If ⬔2 is complementary to ⬔3, ⬔1 is
complementary to ⬔2, and m⬔1 35,
what are m⬔2 and m⬔3? 55, 35
9. What is the value of x if ⬔PQR and ⬔SQT
are vertical angles and m⬔PQR 47 and
m⬔SQT 3x 2? 15
10. Find the measure of an angle that is supplementary
to ⬔B if the measure of ⬔B is 58. 122
©
Glencoe/McGraw-Hill
T17
Geometry: Concepts and Applications
3-7
NAME ______________________________________DATE __________PERIOD______
Practice
Student Edition
Pages 128–133
Perpendicular Lines
៭៮៬
AG ⊥ ៭៮៬
CE , ៭៮៬
AC ⊥ ៭៮៬
BF and point B is the midpoint of ៭៮៬
AC .
Determine whether the following is true or false.
1. ⬔1 ⬵ ⬔CBD true
2. ⬔1 is a right angle. true
3. ⬔2 and ⬔3 are complementary
angles. false
4. m⬔GDF m⬔FDE 90
5. ⬔1 ⬵ ⬔5
true
true
៭៮៬ is the only line perpendicular
6. AC
៭៮៬ at B. true
to BF
7. ⬔3 is an acute angle. false
8. ⬔1 ⬵ ⬔2
false
9. ⬔2 ⬵ ⬔6
true
៭៮៬. true
៭៮៬ is perpendicular to DE
10. AG
11. Name four right angles. Sample answer: ⬔1, ⬔5, ⬔CBD, ⬔EDG
12. Name a pair of supplementary angles. Sample answer: ⬔2 and ⬔3
13. If m⬔3 120, find m⬔2.
60
14. Which angle is complementary to ⬔FDE? ⬔GDF
15. If m⬔6 45, find m⬔2.
©
Glencoe/McGraw-Hill
45
T18
Geometry: Concepts and Applications