The Polygon Angle-Sum Theorems Worksheet With Answers (Page 7 of 8) in pdf

4. Assess

Reteach

Algebra

Find each missing angle measure. Then name the polygon.

47.

48.

49.

48. w

72, x

59,

100

121; k

49, z

PowerPoint

Lesson Quiz

110

13)

10)

103; z

70; quad.

36, 2x

72, 3x

108,

For Exercises 1 and 2, if the figure

144; quad.

is a polygon, name it by its

Open-Ended

Sketch each ﬁgure described in Exercises 50–53.

vertices and identify its sides. If

Problem Solving Hint

50. a quadrilateral that is not equiangular

50–53. See back of book.

the figure is not a polygon,

explain why not.

In Exercises 51-53,

51. an equiangular quadrilateral that is not regular

55. Answers may vary.

sketch a ﬁgure to meet

Sample: The ﬁgure is a

the ﬁrst condition.

52. an equilateral polygon that is not equiangular

convex equilateral

Then adjust it to meet

quadrilateral. The sum of

53. an equiangular polygon that is not equilateral

the second condition.

its angles is 2 180 or 360.

Critical Thinking

54.

Ellen says she has another

54. Yes; the sum of the

way to ﬁnd the sum of the measures of the

quadrilateral ABCD;

measures of ' at the

angles of a polygon. She picks a point inside

int. point is 360. The

the polygon, draws a segment to each vertex,

sum of the measures

counts the number of triangles, multiplies

of all the > is 180n.

by 180, and then subtracts 360. Does her

180n

360

2)180

method work? Explain.

See left.

55.

Writing

Tell what you know about the ﬁgure

at the right.

See above right.

not a polygon because two

56. The measure of an interior angle of a regular polygon is three times the measure

sides intersect at a point other

of an exterior angle of the same polygon. What is the name of the polygon?

than endpoints

octagon

Challenge

57. a.

Graphing Calculator

Find the measure

3. Find the sum of the measures

of an angle of a regular n-gon for

of the angles in an octagon.

n = 20, 40, 60, 80,

, 200. Record

1080

your results to the nearest tenth as

4. A pentagon has two right

ordered pairs in the form (n, measure

angles, a 100° angle and

of each angle).

See margin p. 162.

a 120° angle. What is the

b. Plot the ordered pairs using a window

Xmin = 0

Ymin = 160

measure of its fifth angle?

140

like the one shown at the right.

See back of

Xmax = 200

Ymax = 184

book.

Data Analysis

Based on the graph

ABCDEFGHIJ is a regular decagon.

Xscl = 20

Yscl = 4

from part (b), make a statement about

5. Find m&ABC.

144

the measure of an angle of a regular 1000-gon.

c–d. See margin p. 162.

6. &XBC is an exterior angle at

d. Is there a regular n-gon with an angle of 180 ? Explain.

vertex B. Find m&XBC.

58. a. Explain why the measure of an angle of a regular n-gon is given by the

180(n

360

180n

360

and 180 -

formulas

[180(n

2)]

180

To graph the ordered pairs,

Alternative Assessment

b. Use the second formula to explain what happens to the measures in the

use

and STAT PLOT on

angles of regular n-gons as n becomes a large number. Explain also what

your graphing calculator.

Have students draw a polygon with

happens to the polygons.

See margin p. 162.

5 sides and a polygon with 8 sides.

59. Two rays bisect two consecutive angles of a regular decagon and intersect in

For each polygon, students should

the decagon’s interior. Find the measure of the acute angles formed by the

show the exterior angles and find

For: Graphing calculator

intersecting rays.

the sum of the interior angles and

procedures

Web Code: aue-2120

the sum of the exterior angles.

Draw, if possible, the concave quadrilateral described. If not possible, explain.

Then have them write a paragraph

60–63. See margin.

60. with two pairs of congruent

61. with two pairs of congruent

explaining how the sums illustrate

adjacent sides

opposite sides

the Polygon Angle-Sum Theorem

and the Exterior Angle-Sum

62. with three congruent sides

63. with four congruent sides

Theorem.

163

Lesson 3-5

The Polygon Angle-Sum Theorems

lesson quiz,

, Web Code: aua-0305

60 – 63. Answers may vary.

61. Not possible; opp. sides

63. Not possible; opp. and

Samples are given.

would overlap.

adj. sides would overlap.

60.

62.

163

The Polygon Angle-Sum Theorems Worksheet With Answers Page 7

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