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Prealgebra

Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price

Chapter 10

Two-Dimensional Figures

Educators


Problem 1

In the figure at the right, $\ell \| m$ and $k$ is a transversal. If $m \angle 1=56^{\circ},$ find the measure of each angle.
$$\angle 2$$

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Numerade Educator

Problem 2

In the figure at the right, $\ell \| m$ and $k$ is a transversal. If $m \angle 1=56^{\circ},$ find the measure of each angle.
$$\angle 3$$

Anna J.
Numerade Educator

Problem 3

In the figure at the right, $\ell \| m$ and $k$ is a transversal. If $m \angle 1=56^{\circ},$ find the measure of each angle.
$$\angle 4$$

Anna J.
Numerade Educator

Problem 4

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 5

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 6

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 7

If $m \angle N=3 x$ and $m \angle M=2 x$ and $\angle M$ and $\angle N$ are supplementary, what is the measure of each angle?

Anna J.
Numerade Educator

Problem 8

In the figure at the right, $g \| h$ and $t$ is a transversal. If $m \angle 4=53^{\circ},$ find the measure of each angle.
$$\angle 1$$

Anna J.
Numerade Educator

Problem 9

In the figure at the right, $g \| h$ and $t$ is a transversal. If $m \angle 4=53^{\circ},$ find the measure of each angle.
$$\angle 5$$

Anna J.
Numerade Educator

Problem 10

In the figure at the right, $g \| h$ and $t$ is a transversal. If $m \angle 4=53^{\circ},$ find the measure of each angle.
$$\angle 7$$

Anna J.
Numerade Educator

Problem 11

In the figure at the right, $g \| h$ and $t$ is a transversal. If $m \angle 4=53^{\circ},$ find the measure of each angle.
$$\angle 8$$

Anna J.
Numerade Educator

Problem 12

In the figure at the right, $g \| h$ and $t$ is a transversal. If $m \angle 4=53^{\circ},$ find the measure of each angle.
$$\angle 2$$

Anna J.
Numerade Educator

Problem 13

In the figure at the right, $g \| h$ and $t$ is a transversal. If $m \angle 4=53^{\circ},$ find the measure of each angle.
$$\angle 3$$

Anna J.
Numerade Educator

Problem 14

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 15

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 16

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

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Numerade Educator

Problem 17

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 18

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 19

Find the value of $x$ in each figure.
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 20

Find $m \angle A$ if $m \angle B=17^{\circ}$ and $\angle A$ and $\angle B$ are complementary.

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Problem 21

Angles $P$ and $Q$ are supplementary. Find $m \angle P$ if $m \angle Q=139^{\circ} .$

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Numerade Educator

Problem 22

Angles $J$ and $K$ are complementary. If $m \angle J=x-9$ and $m \angle K=x+5,$ what is the measure of each angle?

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Numerade Educator

Problem 23

Find $m \angle E$ if $\angle E$ and $\angle F$ are supplementary, $m \angle E=2 x+15,$ and $m \angle F=5 x-38$.

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Numerade Educator

Problem 24

ALGEBRA In the figure at the right, $m \| \ell$ and $t$ is a transversal. Find the value of $x$ for each of the following.
(FIGURE NOT COPY)
$$m \angle 2=2 x+3 \text { and } m \angle 4=4 x-7$$

Anna J.
Numerade Educator

Problem 25

ALGEBRA In the figure at the right, $m \| \ell$ and $t$ is a transversal. Find the value of $x$ for each of the following.
(FIGURE NOT COPY)
$$m \angle 8=4 x-32 \text { and } m \angle 5=5 x+50$$

Anna J.
Numerade Educator

Problem 26

To measure the angle between a sloped cathedral ceiling and a wall, a carpenter uses a plumb line (a string with a weight attached) as shown. If $m \angle Y X B=68^{\circ},$ what is $m \angle X B C ?$ Explain your reasoning.

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Problem 27

The measure of the supplement of an angle is $15^{\circ}$ less than four times the measure of the complement. Find the measure of the angle.

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Numerade Educator

Problem 28

Use the clock showing 6 o'clock and 10 seconds.
Find $m \angle W X Y$ and $m \angle Y X Z$

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Numerade Educator

Problem 29

Use the clock showing 6 o'clock and 10 seconds.
Find the time that will show $m \angle W X Y+m \angle Y X Z=90^{\circ}$

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Numerade Educator

Problem 30

Angles $R$ and $S$ are complementary. The ratio of their measures is 4:5. Find the measure of each angle.

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Numerade Educator

Problem 31

Use the graphs.
(GRAPH NOT COPY)
How are each pair of graphs related?

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Problem 32

Use the graphs.
(GRAPH NOT COPY)
What seems to be true about the slopes of the graphs?

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Problem 33

Use the graphs.
(GRAPH NOT COPY)
MAKE A CONIECTURE about the slopes of the graphs of perpendicular lines.

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Problem 34

Use the graphs.
(GRAPH NOT COPY)
OPEN ENDED Draw a pair of adjacent, supplementary angles.

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Problem 35

Use the graphs.
(GRAPH NOT COPY)
CHALLENGE Suppose two parallel lines are cut by a transversal. How are the interior angles on the same side of the transversal related?

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Problem 36

Use the graphs.
(GRAPH NOT COPY)
Writing in Math How are parallel lines and angles related? Illustrate with a drawing of parallel lines intersected by a transversal and a list of the congruent and supplementary angles.

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Numerade Educator

Problem 37

The hedge shears have two different sets of angles. Find $x$
A 32
B 58
C 102
D $121$
(FIGURE NOT COPY)

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Numerade Educator

Problem 38

Which angles are NOT supplementary?
$\mathbf{F} \angle E Z C, \angle C Z A \quad \mathbf{H} \quad \angle A Z B, \angle B Z E$ $\mathbf{G} \angle B Z C, \angle C Z D \quad \mathbf{J} \quad \angle D Z E, \angle A Z D$
(FIGURE NOT COPY)

Anna J.
Numerade Educator

Problem 39

At the same time a 40 -foot silo casts a 22 -foot shadow, a fence casts a $3.3 \text {
foot shadow. Find the height of the fence. (lesson } 9.6)$

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Numerade Educator

Problem 40

Two artifacts are found at a dig. If a coordinate plane is set up, one artifact was found at $(1,5)$ and the other artifact was found at $(3,1)$ How far apart were the two artifacts? Round to the nearest tenth. (lesson 9.5 )

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Problem 41

Solve each inequality.
$$5 m<5$$

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Problem 42

Solve each inequality.
$$\frac{a}{-2}>3$$

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Numerade Educator

Problem 43

Solve each inequality.
$$-4 x \geq-16$$

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Problem 44

Use a protractor to draw an angle having each measurement. (pp $757-788$ )
$$20^{\circ}$$

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Numerade Educator

Problem 45

Use a protractor to draw an angle having each measurement. (pp. $757-758$ )
$$45^{\circ}$$

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Numerade Educator

Problem 46

Use a protractor to draw an angle having each measurement. (pp. $757-758$ )
$$65^{\circ}$$

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Numerade Educator

Problem 47

Use a protractor to draw an angle having each measurement. (pp. $757-758$ )
$$145^{\circ}$$

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Numerade Educator

Problem 48

Use a protractor to draw an angle having each measurement. (pp. $757-758$ )
$$170^{\circ}$$

Anna J.
Numerade Educator