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Lesson 12.1 Angles on a Line

Practice 1 Angles on a LineIn each figure, AC is a line. Use a protractor to find the unknown angle measures.

1.

m�DBC �

m�DBA �

m�DBC � m�DBA � �

�

2.

Angles

Cha

pter

131

m�x �

m�y �

m�x � m�y � �

�

B CA

D

A

Bx

yC

D

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09(M)MIF2015CC_WBG5B_Ch12.indd 131 29/04/13 2:30 PM

Chapter 12 Angles

AC is a line. Use a protractor to find the unknown angle measures.

3. m�p �

m�q �

m�r �

m�p � m�q � m�r � � �

�

Name the angles on each line.

4. XZ is a line.

W

Y Z X

5. PR is a line.

QR

Pa

bc

ST

qp r

A B C

E

D

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Lesson 12.1 Angles on a Line

Name each set of angles on a line.

6. AC is a line. 7. AB and CD are lines.

Find the unknown angle measures.

8. AC is a line. Find the measure of �DBC.

D

B CA

125°

9. EG is a line. Find the measure of �HFE.

m�HFE �

H

E

42°

I

F G

C

A

qr

st

p

D

E

F

trp q

s

C

A

D

B

E

m�DBC � 125° � 180°

m�DBC � 180° �

�

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Chapter 12 Angles


10. OQ is a line. Find the measure of �SPT.

P 39°

70°

15°

Q

O

R S

T

m�SPT �

11. AC is a line. Find the measure of �EBF.

BA

C41°

27°D

EF

m�EBF �

12. JK is a line. Find the measures of �y and �z.

72°y

z

36°80°J

I

G H

K

m�y �

m�z �

13. EF and GH are lines. Find the measures of �a and �b.

20°50°

GH

IJ

E

F

ab

m�a �

m�b �

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Lesson 12.2 Angles at a Point

Practice 2 Angles at a PointIn each figure, the rays meet at a point. Use a protractor to find unknown angle measures.

1.

a

cb m�a �

m�b �

m�c �

m�a � m�b � m�c � � �

�

2.

m�AOB �

m�BOC �

m�COD �

m�DOE �

m�AOE �

m�AOB � m�BOC � m�COD � m�DOE � m�AOE

� � � � �

�

B

C O

D

E

A

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Chapter 12 Angles

Name the angles at a point.

3.

b

a

c

4.

5.

c

b

a

d

6.

k h

gf

e

O

W Z

X

Y

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Lesson 12.2 Angles at a Point


7. Find the measure of �AOB. 8. Find the measure of �a.

O 142°

104°

B

A

C

a

m�AOB � m�a �

9. Find the measure of �b. 10. Find the measure of �c.

b

310°

40°26°

c

m�b � m�c �

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Chapter 12 Angles


11. Find the measure of �q. 12. Find the measure of �r.

q

83°37°

112°r

m�q � m�r �

13. Find the measure of �a.

a

164°

m�a �

14. PR and TU meet at Q. Find the measures of �PQS and �TQR.

Q

T

P 75° R

SU

51°

m�PQS �

m�TQR �

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Lesson 12.3 Vertical Angles

Practice 3 Vertical AnglesComplete.

1. AB and CD meet at O. Use a protractor to find unknown angle measures.

m�w �

m�x �

m�y �

m�z �

m� � m�

� and � are vertical angles.

m� � m�


2. XZ and VW meet at Y. Use a protractor to find unknown angle measures.

m�XYW �

m�WYU �

m�UYZ �

m�ZYV �

m�VYX �



C

A

B

OD

z

yw

x

X W

U

ZV

Y

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Chapter 12 Angles

Complete.

3. Look at the star and its marked angles. In the table below, write three sets of a. angles on a line, b. angles at a point, c. vertical angles.

u

x w

k

lj

i

h

e

gf

mp

on

qr

ts

b a

dc vy

Angles on a Line Angles at a Point Vertical Angles

�b and �c �a, �b, �c, and �d �a and �c

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Draw.

4. Draw rays at P to form a. an angle whose measure forms a sum of 180° with the measure of �x, b. an angle whose measure is equal to the measure of �x. (Do not use a protractor to draw the angles.)

a.

xP

b.

Px

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Chapter 12 Angles


5. AB and CD meet at O. Find the measure of �COB.

130°

OA

CB

D

m�COB �

6. EF and GH meet at O. Find the measures of �GOF and �EOH.

E

G

O

F

H

48° m�GOF �

m�EOH �

7. RS and PQ meet at N. Find the measures of �PNR, �RNQ, and �QNS.

m�PNR �

m�RNQ �

m�QNS �

160°

P

S

Q

R

N©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

142




8. JK and LM meet at O. Find the measure of �NOK.

108°

52° OL

N K

M

J

m�NOK �

9. AB , CD, and EF meet at O. Find the measure of �x.

C

E B

A F

50°

120°

O

D

x

m�x �

10. AB and CD meet at O. Find the measure of �w.

75°A

C

DB

wO

m�w �

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Chapter 12 Angles


11. QR and ST meet at O. Find the measures of �QOS, �TOR, and �SOR.

SQ

70°R

T

O

m�QOS �

m�TOR �

m�SOR �

12. AB and CD meet at O. Find the measures of �p, �q, and �r.

25°

A

C r

qp

D

B

O

m�p �

m�q �

m�r �

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13. UV , WX, and YZ meet at O. Find the measure of �UOW.

72°68°O

XVY

W

U Z

m�UOW �

14. AB , CD, and EF meet at O. Find the measures of �x and �y.

x y

60°

F B C

A E

D

O

m�x �

m�y �

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Chapter 12 Angles

Check the box for each correct statement.Then explain your answer.

1. XY is a line.

a b

X Y

m�a is more than 90°.

If m�a � m�b, then m�a � 45°.

2. AB and CD meet at O.

m�e � m�h

m�f � m�g � m�j

m�e � m�g

O

A C

BD

e

fg

h

j

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Chapter 12 Angles

Put On Your Thinking Cap!

Find the unknown angle measures. Explain.

1. GJ is a line. �LHK is a right angle. Find the measure of �LHJ.

LH

JK

155°

G

2. MN and XY meet at O and m�a � m�b. Find the measure of �c.

M

X

O

cb

a

Y

N

P

Challenging Practice

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Chapter 12 Angles

3. AC is a line. �ABE and �DBF are right angles. Find the measure of �FBC.

4. AB and WX meet at O. �COB and �YOX are right angles. Find the measures of �AOX and �COY.

A

B

C

26°

F

ED

A

W X

BY

C

O

56°

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Chapter 12 Angles

Put On Your Thinking Cap!

Solve.

1. JK and LM are lines. Check the box for each correct statement.

a. m�p � m�r � m�s

b. m�s � m�p � m�r

c. m�q � 180° � m�p

d. m�r � m�s � m�p � m�q

2. AB , CD , and EF meet at O. Find the sum of the measures of �AOC, �FOD, and �BOE.

m�AOC � m�FOD � m�BOE �

O

E B

D

FA

C

Problem Solving

sr

t

q

M

K

p

J

L

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Chapter 12 Angles

3. ABCD is a square. BE is a ray. Find the measure of �x.

A

B

D

C

xE

135°

4. How many degrees does the hour hand of a clock turn between 3 P.M. and 7:30 P.M.?

5. AB is a line. The measures of �a and �b are whole numbers.

A B

ab

If the measure of �b is twice that of �a, find the measures of �a and �b.

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p t h angles - thorp o a elementary scholastic academyj l i h e g f m p o n r q s t b a y c d v...

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