Geometry

Edward Burger, David J. Chard,Earlene J. Hall

Chapter 6 Polygons and Quadrilaterals - all with Video Answers

Educators

Section 1

Properties and Attributes of Polygons

00:54

Problem 1

Explain why an equilateral polygon is not necessarily a regular polygon.

Charles Carter

Numerade Educator

00:46

Problem 2

Tell whether each outlined shape is a polygon. If it is a polygon, name it by the number of its sides.
(IMAGE CANNOT COPY)

Charles Carter

Numerade Educator

00:32

Problem 3

Tell whether each outlined shape is a polygon. If it is a polygon, name it by the number of its sides.
(IMAGE CANNOT COPY)

Charles Carter

Numerade Educator

00:32

Problem 4

Tell whether each outlined shape is a polygon. If it is a polygon, name it by the number of its sides.
(IMAGE CANNOT COPY)

Charles Carter

Numerade Educator

00:18

Problem 5

Tell whether each outlined shape is a polygon. If it is a polygon, name it by the number of its sides.
(IMAGE CANNOT COPY)

Charles Carter

Numerade Educator

00:25

Problem 6

Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:51

Problem 7

Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:38

Problem 8

Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

02:23

Problem 9

Find the measure of each interior angle of pentagon $A B C D E$.

Charles Carter

Numerade Educator

01:05

Problem 10

Find the measure of each interior angle of a regular dodecagon.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:56

Problem 11

Find the sum of the interior angle measures of a convex 20 -gon.

Charles Carter

Numerade Educator

01:53

Problem 12

Find the value of $y$ in polygon $J K L M$ (FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:51

Problem 13

Find the measure of each exterior angle of a regular pentagon.

Charles Carter

Numerade Educator

00:17

Problem 14

Safety Use the photograph of the traffic sign.
Name the polygon by the number of its sides.

Charles Carter

Numerade Educator

01:36

Safety Use the photograph of the traffic sign.
In the polygon, $\angle P, \angle R,$ and $\angle T$ are right angles, and $\angle Q \cong \angle S .$ What are $\mathrm{m} \angle Q$ and $\mathrm{m} \angle S ?$

Charles Carter

Numerade Educator

00:27

Problem 16

Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:24

Problem 17

Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:37

Problem 18

Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:53

Problem 19

Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:33

Problem 20

Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

00:43

Problem 21

Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
(FIGURE CANNOT COPY)

Charles Carter

Numerade Educator

02:02

Problem 22

Find the measure of each interior angle of quadrilateral $R S T V$.

Charles Carter

Numerade Educator

01:21

Problem 23

Find the measure of each interior angle of a regular 18 -gon.

Charles Carter

Numerade Educator

00:41

Problem 24

Find the sum of the interior angle measures of a convex heptagon.

Charles Carter

Numerade Educator

00:46

Problem 25

Find the measure of each exterior angle of a regular nonagon.

Charles Carter

Numerade Educator

00:56

Problem 26

A pentagon has exterior angle measures of $5 a^{\circ}, 4 a^{\circ}, 10 a^{\circ}, 3 a^{\circ},$ and $8 a^{\circ} .$ Find the value of $a$.

Charles Carter

Numerade Educator

01:01

Problem 27

The folds on the lid of the gift box form a regular hexagon. Find each measure.
$$\mathrm{m} \angle J K M$$

Charles Carter

Numerade Educator

00:40

Problem 28

The folds on the lid of the gift box form a regular hexagon. Find each measure.
$$\mathrm{m} \angle M K L$$

Charles Carter

Numerade Educator

01:34

Problem 29

Find the value of $x$ in each figure.
(FIGURE CAN'T COPY)

Charles Carter

Numerade Educator

02:10

Problem 30

Find the value of $x$ in each figure.
(FIGURE CAN'T COPY)

Charles Carter

Numerade Educator

00:49

Problem 31

Find the value of $x$ in each figure.
(FIGURE CAN'T COPY)

Charles Carter

Numerade Educator

01:10

Problem 32

Find the number of sides a regular polygon must have to meet each condition.
Each interior angle measure equals each exterior angle measure.

Charles Carter

Numerade Educator

00:53

Problem 33

Find the number of sides a regular polygon must have to meet each condition.
Each interior angle measure is four times the measure of each exterior angle.

Charles Carter

Numerade Educator

01:19

Problem 34

Find the number of sides a regular polygon must have to meet each condition.
Each exterior angle measure is one eighth the measure of each interior angle.

Charles Carter

Numerade Educator

00:45

Problem 35

Name the convex polygon whose interior angle measures have each given sum.
$$540^{\circ}$$

Charles Carter

Numerade Educator

00:40

Problem 36

Name the convex polygon whose interior angle measures have each given sum.
$$900^{\circ}$$

Charles Carter

Numerade Educator

00:44

Problem 37

Name the convex polygon whose interior angle measures have each given sum.
$$1800^{\circ}$$

Charles Carter

Numerade Educator

00:45

Problem 38

Name the convex polygon whose interior angle measures have each given sum.
$$2520^{\circ}$$

Charles Carter

Numerade Educator

00:57

Problem 39

An exterior angle measure of a regular polygon is given. Find the number of its sides and the measure of each interior angle.
$$120^{\circ}$$

Charles Carter

Numerade Educator

00:45

Problem 40

An exterior angle measure of a regular polygon is given. Find the number of its sides and the measure of each interior angle.
$$72^{\circ}$$

Charles Carter

Numerade Educator

00:36

Problem 41

An exterior angle measure of a regular polygon is given. Find the number of its sides and the measure of each interior angle.
$$36^{\circ}$$

Charles Carter

Numerade Educator

00:44

Problem 42

An exterior angle measure of a regular polygon is given. Find the number of its sides and the measure of each interior angle.
$$24^{\circ}$$

Charles Carter

Numerade Educator

00:41

Problem 43

Which conclusion is incorrect? Explain the error.
A. The figure is a polygon. B. The figure is not a polygon.

Charles Carter

Numerade Educator

06:40

Problem 44

Graph the polygon formed by the points $A(-2,-6), B(-4,-1)$ $C(-1,2), D(4,0),$ and $E(3,-5) .$ Estimate the measure of each interior angle. Make a conjecture about whether the polygon is equiangular. Now measure each interior angle with a protractor. Was your conjecture correct?

Charles Carter

Numerade Educator

03:07

Problem 45

This problem will prepare you for the Concept Connection on page $406 .$ In this quartz crystal, $\mathrm{m} \angle A=95^{\circ}, \mathrm{m} \angle B=125^{\circ}$ $\mathrm{m} \angle E=\mathrm{m} \angle D=130^{\circ},$ and $\angle C \cong \angle F \cong \angle G$.
a. Name polygon $A B C D E F G$ by the number of sides.
b. What is the sum of the interior angle measures of $A B C D E F G ?$
c. Find $\mathrm{m} \angle F$

Charles Carter

Numerade Educator

00:34

Problem 46

The perimeter of a regular polygon is 45 inches. The length of one side is 7.5 inches. Name the polygon by the number of its sides.

Charles Carter

Numerade Educator

00:38

Problem 47

Draw an example of each figure.
a regular quadrilateral.

Charles Carter

Numerade Educator

00:56

Problem 48

Draw an example of each figure.
an irregular concave heptagon.

Charles Carter

Numerade Educator

00:44

Problem 49

Draw an example of each figure.
an irregular convex pentagon.

Charles Carter

Numerade Educator

00:43

Problem 50

Draw an example of each figure.
an equilateral polygon that is not equiangular.

Charles Carter

Numerade Educator

00:58

Problem 51

Use the terms from the lesson to describe the figure as specifically as possible.

Charles Carter

Numerade Educator

00:58

Problem 52

What geometric figure does a regular polygon begin to resemble as the number of sides increases?

Charles Carter

Numerade Educator

00:50

Problem 53

Which terms describe the figure shown?
I. quadrilateral II. concave III. regular
A. I only
B. I and II
C. II only
D. I and III

Charles Carter

Numerade Educator

01:34

Problem 54

Which statement is NOT true about a regular 16 -gon?
F. It is a convex polygon.
G. It has 16 congruent sides.
H. The sum of the interior angle measures is $2880^{\circ} .$
J. The sum of the exterior angles, one at each vertex, is $360^{\circ} .$

Charles Carter

Numerade Educator

02:06

Problem 55

In polygon $A B C D, m \angle A=49^{\circ}, m \angle B=107^{\circ},$ and $m \angle C=2 m \angle D .$ What is $m \angle C ?$.
A. $24^{\circ}$
B. $68^{\circ}$
C. $102^{\circ}$
D. $136^{\circ}$

Charles Carter

Numerade Educator

01:47

Problem 56

The interior angle measures of a convex pentagon are consecutive multiples of 4. Find the measure of each interior angle.

Charles Carter

Numerade Educator

03:20

Problem 57

Polygon $P Q R S T$ is a regular pentagon. Find the values of $x, y,$ and $z .$

Charles Carter

Numerade Educator

03:57

Problem 58

Polygon $A B C D E F G H J K$ is a regular decagon. Sides $\overline{A B}$ and $\overline{D E}$ are extended so that they meet at point $L$ in the exterior of the polygon. Find $\mathrm{m} \angle B L D$.

Charles Carter

Numerade Educator

03:11