PACKET - Angles

Name _______________________________ HR ______

Test Date __________________________

ANGLES

UNIT 9

MATH PACKET

Understanding and Measuring Angles

QUICK CHECK

▶_{Complete with point, line, or line segment.}

A is an exact location in space.

A is part of a line with two endpoints.

A is a straight path continuing without end in two directions.

▶_{Decide whether each figure forms an angle. Explain your answer.}

▶_{Name the angle.}

(1)

(2)

(3)

(6) (5)

(4) Explain: ______________________________ ______________________________________ ______________________________________

▶_{Mark an angle in each shape.}

▶_{Decide whether the line segments in each angle form a right angle. Answer yes or}

no. Use a piece of folded paper to help you, if needed.

▶_{Look at the angles. Then answer the questions that follow.}

Which angles are right angles?

Which angles measure less than a right angle?

Which angles measure greater than a right angle?

(7) (8)

(11) (10)

(9)

(12)

(13)

(14)

A

F

D

E

LESSON 9.1 - UNDERSTANDING & MEASURING ANGLES

VOCABULARY: • ray

• vertex

• protractor

• degrees

• inner scale

• outer scale

• acute angle

GUIDED LEARNING

▶_{Name the angles.}

▶_{Name the angles.}

▶_{Name the angles labeled at the vertices A, B, C, and D in another way.}

P

R Q

S

(1) or

(4) (3)

(2) Angle at P:

∠

Angle at R:

∠

Angle at S:

∠

Angle at Q:

∠

or or or (11) (10) (9) (8) (7) (6) (5)

or or or

A C B X Z Y G E F

∠

x

:

∠

∠

r

:

∠

∠

y

:

∠

∠

z

:

∠

or

or

or

READ A PROTRACTOR

▶_{FIRST: Identify the TYPE of angle!}

▶_Complete.

(1)

The measure of DEF is less than that of a right angle. It is 70º.

Measure of

∠

DEF =

Since

∠

DEF is an ACUTE angle, read the measure on the outer scale.

(2)

The measure of

∠

ABC is

of a turn. The measure of

∠

PQR is

of a turn.

(3) Measure

∠

GHK. _{Is the measure of}

_∠

_{GHK less than or greater} than 90º?

The measure of

∠

GHK is degrees.

Measure of

∠

GHK =

H K

G

Measure

∠

DEF.

D

Did you read the inner or outer scale? Explain your answer.

▶_{Find the measure of each angle.}

(4) Is the measure of

∠

JKL less than or greater than 90º?

The measure of

∠

JKL is degrees.

Measure of

∠

JKL = Measure

∠

JKL.

(5) (6)

J

L K

Measure of

∠

XYZ= Measure of

∠

ABC=

▶_{An angle with a measure less}

than 90º is an acute angle. ▶ _{An angle with a measure}

greater than 90º but less than 180º is an obtuse angle.

▶_{Name and measure the}

angles.

Name two angles that are right angles.

Name four angles that are acute angles. What are the measures of these angles?

Name four angles that re obtuse angles. What are the measures of these angles?

▶_{Use a protractor to find the measure of each angle.}

LET’S PRACTICE

(1)

(2)

(3)

(4) (5)

LESSON 9.2 - DRAWING ANGLES TO 180

º

▶_{An angle with a measure of 180º is}

▶_{Use a protractor to to draw an angle with the measurements shown.}

∠

DEF measures 50º

∠

RST measures 95º

∠

LMN measures 125º

(1) (2)

LESSON 9.3 - TURNS & ANGLE MEASURES

▶_{To find a fraction of a circle, divide 360 by the denominator of the fraction.}

▶_{For instance, if you are given a problem asking for the number of degrees in}

C

_{of a}

circle, divide 360 ÷ 3 = 120.

measure circles in degrees & fractions

Find the number of degrees of each part of the circle as requested. Tell what kind of angle is formed by one part of the circle: acute, right, obtuse, or straight.

Measure of angle:

Type of angle:

Measure of angle:

Type of angle:

Measure of angle: _{Measure of angle:} (1)

(4) (3)

measure circles in degrees & fractions -

C

on

tinued

Measure of angle:

Type of angle:

Measure of angle:

Type of angle:

Measure of angle:

Type of angle:

Measure of angle:

Type of angle: (5)

(7) (8)

GUIDED LEARNING -

Use Expl

or

ag

on

s

Complete using

A

,

F

,

H

, or 1.

(a) Two right angles make up a turn.

(b) Four right angles is the same as full turn.

(c) 270º is of a full turn.

(d) 93º is between a turn and a turn.

(e) 200º is between a turn and a turn.

(2) 100º is exactly of a full turn.

USE A PROTRACTOR TO SHOW ANGLE MEASURES CAN BE ADDED

An angles can be divided up into non-overlapping parts. In the diagram below,

∠

CBA is

divided up into two non-overlapping angles,

∠

CBD and

∠

DBA.

(1)

A

D

*You can see that the measure of

∠

CBD = 40º, and the measure of

∠

DBA = 30º.

FIND THE UNKNOWN ANGLE

▶_{Find the unknown angle measurements.}

• ∠LMN =

• ∠QMN =

• Therefore, ∠LMQ =

L

(1)

M N

Q

• ∠XYZ =

• ∠TYZ =

• Therefore, ∠XYT =

X T Z Y (2) S T U G

• ∠STU =

• ∠GTU =

FIND THE UNKNOWN ANGLE using addition & subtraction

▶_{You can write the measure of a angle as “m}∠PXR”.

▶_Complete. (Sample)

(1)

m∠PXR = m∠PXQ + m∠QXR = 45º + 78º

= 123º

(Sample)

∠y + 56º = 98º So, ∠y = 98º — 56º

= 42º

(2)

m∠AOC = 90º m∠BOC = 35º m∠AOB =

m∠XOY = 125º m∠YOZ = 15º m∠XOZ =

(3) _{∠AOB is a straight angle.} m∠BOT = 68º

▶_{Use the Exploragons to answer the questions.}

How many turns are in three right angles? How many turns are in four right angles? What fraction of full turn is two right angles?

▶_{Use the circles to draw the following angles.}

Angle between a

H

-turn and a full turn.

Angle between a

A

-turn and a full turn.

Angle between a

F

-turn and a

A

-turn.

LET’S PRACTICE

(1)

(2)

(3)

(4)

(5)

▶_{Find the measure of the unknown angle.}

Find the measure of ∠EPG. (8) The measure of ∠LQN is 84º.

Find the angle measure x.

Joshua stands in the center of the circle shown in the picture.

If Joshua is facing Blake and turns around until he is looking at Ian, what fraction of a turn will he make?

What angle does Joshua turn through if he moves: from looking at Perry to looking at Ian? from looking at Roy to looking at Perry? (7)

Problem Solve

(1)

(2)

CHAPTER WRAP UP: ANGLES

▶_{STUDY GUIDE: You have learned:}

➊

➋

➌

CHAPTER REVIEW

▶_{Find the correct ray.}

Which ray forms an angle measure of 85º with ray AX?

Which ray forms an angle measure of 120º with ray PQ?

Use the triangle. Name the vertices of the triangle A, B, and C. Write x, y, and z inside the triangle so that:

(1)

(2)

(3)

▶_{Which scale would you use to read the angles shown? Complete the following}

questions.

▶_{Use a protractor to measure the angles. Then identify the acute angles and obtuse}

angles.

▶_{Fill in the blanks.}

H

_{-turn is 90º is -turn}

One full turn is A 30º angle is of a turn.

(4) (5)

a) What type of angle is ∠ABC? b) Use inner scale or outer scale? c) ∠ABC measures:

A C B L N M º

a) What type of angle is ∠LMN? b) Use inner scale or outer scale? c) ∠LMN measures: º

Angle measure w =

Angle measure x =

Angle measure y =

Angle measure z =

(14)

m∠AOC = 110º m∠BOC = º

(15)

Find m∠XOZ

m∠XOZ = º

Su Jin folded a paper square in half to form a right triangle, as shown. What is the measure of ∠BDC? (16)

º

B

C

D

(17) On a clock face, the measure of ∠AOB is shown as 90º. Explain how to find the measure of the other ∠AOB.

On three copies of this clock face, use the center as the common point and draw 5 angles

a) which are right angles b) which are 180º

▶_{Draw angles with these measures. FIRST, name the type of angle!}

65º __________

170º __________

85º __________ (18)

(19)