Lesson 11.

4
Name
Join and Separate Angles Measurement and Data—
Essential Question How can you determine the measure of an angle 4.MD.C.7
separated into parts? MATHEMATICAL PRACTICES
MP2, MP4, MP5

Hands
Investigate
Investigate On

Materials ■ construction paper ■ scissors ■ protractor

A. Use construction paper. Draw an angle that measures
exactly 70°. Label it ∠ABC.

B. Cut out ∠ABC.

C. Separate ∠ABC by cutting it into two parts.

Begin cutting at the vertex and cut between
the rays.

What figures did you form? ___

D. Use a protractor to measure the two angles you formed.

Record the measures. __

E. Find the sum of the angles you formed.

You can think of /ABC
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (r) ©Houghton Mifflin Harcourt

_+_=_ as the whole and the two

part + part = whole angles you formed as the
parts of the whole.
F. Join the two angles. Compare m∠ABC to the sum of the
measures of its parts. Explain how they compare.

Chapter 11 621
 Draw Conclusions

1. What if you cut ∠ABC into two different angles? What can you
conclude about the sum of the measures of these two angles?
Explain.

2. Seth cut ∠ABC into 3 parts. Draw a model that

SMARTER

shows two different ways he could have separated his angle.

3. Write a sentence that compares the measure of an angle to the

sum of its parts.

Make
Make Connections
Connections
B
Materials ■ protractor D
You can write the measure of the angles shown
C
in a circle as a sum.

STEP 1 Use a protractor to find the measure of each angle.

A
© Houghton Mifflin Harcourt Publishing Company

STEP 2 Label each angle with its measure. Math MATHEMATICAL PRACTICES 6
Talk
Use Math Vocabulary
STEP 3 Write the sum of the angle measures as an equation.
Describe the angles shown
in the circle above using
_+_+_=_ the words whole and part.
part + part + part = whole

622
 Name

MATH
M
Share
Share and
and Show
hhow
Sh BOARD
B

Add to find the measure of the angle. Write an equation to record your work.
1. 2. 3.
10°
P
L 27°
43° 55°
37° S 78°
Q T 90° H R
J K

m∠PQT = _ m∠JKL = _ m∠RHS = _

Use a protractor to find the measure of each angle. Label each angle with its measure.
Write the sum of the angle measures as an equation.
4. 5. Y
X
J K
Z V
L

M W

OqnakdlRnkuhmf¤@ookhb`shnmr
OqnakdlRnkuhmf¤@ookhb`shnmr

6. MATHEMATICAL
PRACTICE 4 Use Diagrams What is 7. DEEPER Look back at Exercise 1. Suppose
m∠QRT? you joined an angle measuring 10° to ∠PQT.
Draw the new angle, showing all three parts.
D R Q
© Houghton Mifflin Harcourt Publishing Company

What type of angle is formed?

75° 85° ?
T

Chapter 11 • Lesson 4 623

 MATHEMATICAL PRACTICES COMMUNICA5&
t
1&34E7&3&
t
CONSTRUCT ARGUMENTS

Unlock
Unlock the
the Problem
Problem

8. SMARTER Stephanie, Kay, and Shane each

ate an equal-sized piece of a pizza. The measure
of the angle of each piece was 45°. When the pieces
were together, what is the measure of the angle
they formed?
a. What are you asked to find?

b. What information do you need to use?

c. Tell how you can use addition to solve the problem.

d. Complete the sentence. The three pieces of pizza formed a angle.

Personal Math Trainer

SMARTER
9. What is the measure of ∠XZW ? Write an 10. What is m∠PRS? Use
equation to record your work. equations to explain and check your
answer.
N
Y
X
42° P
71° 90° 78°
W ?
© Houghton Mifflin Harcourt Publishing Company

Z S R T

624
 Practice and Homework
Name
Lesson 11.4
Join and Separate Angles
COMMON CORE STANDARD—4.MD.C.7
Geometric measurement: understand concepts
Add to find the measure of the angle. Write an of angle and measure angles.
equation to record your work.
1. 2. H 3.
M
C F 140° P
A 20°
G J 30° 90°
50° K 45°
75° L N
B D

50° + 75° = 125°

m/ABD = __
125° m/FGJ = __ m/KLN = __

Use a protractor to find the measure of each C

angle in the circle.
4. m/ABC = __ 5. m/DBE = __

A
B D
6. m/CBD = __ 7. m/EBA = __

Problem E
Problem Solving
Solving

8. Ned made the design at the right. Use a protractor. Find

and write the measure of each of the 3 angles.

________
_
9. Write an equation to find the measure of the
© Houghton Mifflin Harcourt Publishing Company

_ _
total angle.

________

10. WRITE Math How can you use addition and

subtraction to put together and separate measures
of an angle and its parts?

Chapter 11 625
 TEST
Lesson Check (4.MD.C.7)
PREP
1. What is the measure of /WXZ? 2. Write an equation that you can use to find
the m/MNQ.
Y Z P
25°
148° 24°
Q
58° M N
W X

Spiral Review (4.NBT.B.5, 4.NF.B.3d, 4.MD.C.5a, 4.MD.C.5b, 4.G.A.2)

3. Joe bought 6 packages of envelopes. Each __
3 mile on the Lake Trail. Then he
4. Bill hiked 10
package contains 125 envelopes. How many hiked __
5
10 mile on the Rock Trail to get back
envelopes did he buy? to where he started. How many miles did
he hike?

5. Ron drew a quadrilateral with 4 right angles 6. How many degrees are in an angle that
and 4 sides with the same length. What turns through 3_4 of a circle? © Houghton Mifflin Harcourt Publishing Company
figure did he draw?

FOR MORE PRACTICE

GO TO THE
626 Personal Math Trainer