Geometry Polygons Sum of the interior angles of a (n

Name

Geometry Polygons

Sum of the interior angles of a

(n - 2)180

polygon ~,

Sum of the exterior angles of a

360

polygon

Each interior angle of a regular

(n - 2)180

i polygon

Each exterior angle of a regular

360

polygon

Geometry

NAME:

WORKSHEET:

Polygon Angle Measures

PERIOD: __

DATE:

Use the given information to complete the table. Round to the nearest tenth if necessary.

Measure of ONE

Exterior Angle

Measure of ONE

# Sides

Interior Angle

Sum

INTERIOR Angle EXTERIOR Angle

(Regular Polygon)

Sum

(Regular Polygon)

1080

900

5040

1620

150

lO)

120

11)

156

12)

13)

7.2

14)

15)

Geometry

NAME:

WORKSHEET:

Angles of Polygons - Review

PERIOD:

DATE:

USING THE INTERIOR & EXTERIOR ANGLE SUM THEOREMS

The measure of one exterior angle of a regular polygon is given.

Find the nmnbar of sides for each,

a) 72

b) 40

Find the measure of an interior and an exterior angle of a regular 46-gon.

The measure of an exterior angle of a regular polygon is 2x, and the measure of an

interior angle is 4x.

a) Use the relationship between interior and exterior angles to find x.

b) Find the measure of one interior and exterior angle.

c) Find the number of sides in the polygon and the type of polygon.

The measure of one interior angle of a regular polygon is 144

°.

How many sides does it have?

Five angles of a hexagon have measures 100

°,

110

°,

120

°,

130

°,

and 140

°.

What is the measure of the sixth angle?

Find the value ofx.

ABCDE and HIJKL are regular pentagons and AEFGHL is a regular hexagon.

If Z.ABK -=/LKB, find m/_ABK.

Geometry

NAME:

WORKSHEET:

Polygons & lnterior Angles

PERIOD:

DATE:

USING THE INTERIOR ANGLE SUM THEOREM

Since a hexagon has six (6) sides, we can find the sum of all six interior angles by using

n = 6 and:

Sum = (n-2)’180

(6- 2).180

(4)-180

Hexagon Sum

720

All regular polygons are equiangular, therefore, we can find the measure

of each

interior

angle

by:

One

interior angle of a

regular

polygon

- (n - 2). 180

~ [ Sum of all

angles

For a

hexagon:

720

One interior angle =

120

Note:

The previous information could also be used to find the number of sides for a

regular

polygon given the measure of one interior angle.

Example: How many sides does a regular polygon have if one interior angle

measures 157.5

From above:

157,5- (n-2).180

What is the value of n?

157.5n = (n-2)’180

PRACTICE...

Show all work required to complete each of the following.

1) What is another name for a regular quadrilateral?

2) Find the sum of the measures of the interior angles of a convex heptagon.

3) What is the measure of each interior angle of a regular pentagon?

4) The sllnl of the interior angles of a polygon is 1620

°.

How many sides does it have?

Can the interior angles of a polygon have a sum between 4300

and 4400°?

If so, how many sides can it have?

The measure of the interior angle of a regular polygon is 179°. How many sides does it

have?

Is it possible for a regular polygon to have each of its interior angles measure 142°?

Support your answer.

8) Find the value ofx in the figure given.

Geometry

~ = Polygons

Concave pentagon

3. Concave octagon

5. Convex equiangular hexagon

Convex septagon

4. Concave equilateral quadrilateral

6. Convex regular decagon

Classify each diagra~n:

Concave

Equiangular

Hexagon

~onve×

Equilateral

Octagon

Pentagon

Triangle

Regular

dodecagon

decagon

nonagon

10o

11.

13,

Name the

Polygon

~o different

ways° Remember

14.

- this doesn’t mean classify!!

Matching:

16.

lldOdecagon

......

triangle

pentagon

~C. 5

19.

nonagon

D~6

20.

~quadri~ateral

E. 7

21.

lhexagon

F. 8

22.

octagon

G. 9

23Ol

,heptagon

H. 10

24.

decagon

I. 12

25° Name all angles consecutive to ~

Name

two diagonals.

26.

27. Name two consecutive sides.

27. ,9

28.

Explain why the given figure is not a polygon. Your answer must be in

29.

Explain in complete sentences what it means if a polygon is regular.

Sketch an example.

,Geometry . ¯

Find the SUM of the interior angles of each polygon.

odagon

pentagon

hexagon

heptagon

Name

Date

Find the SUM of the exterior angles of each polygon.

octagon

pentagon

What is the measure of EACH interior angle of a regular:

odagon

pentagon

hexagon

decagon

What is the measure of EACH exterior angle of a regular:

octagon

pentagon

hexagon

decagon

Find the measure of the variables.

the measure of the variables.

Find the measure of/-i in each figure,

:/..3. ~

16,

Find the measure ef each angle,

19.

20,

(x +

(2x + 20)

15.

¯ F~nd bach unknown angle measure.

For questions 1 - 4, classify each polygon. Be as specific as possible.

Z1. 0

Z2.

"2, 5. Which of the polygons in 1 - 4 is concave?

2-6.

Given:

~ ~.~..~..." "-~.~.

a) How many different ways can the polygon be named?

b) Name a

pair of consecutive sides.

c) Name a

pair of nonconsecutive vertices.

2.,7. True or Fafse? Every equilateral polygon is equiangular.

~-8. True or False? Every regular polygon is convex.

"2..8. True or False? Every three sided polygon is convex.

310. Sketch a plane figure that is not a polygon and explain

why it is not_.

~ 1. Sketch the following:

a) convex equilateral pentagon

b) concave octagon

c) regular quadrilateral

Interior

Exterior

Sum

360

Each for Regular

(n-2) .180

(n-2)

.180

360

Find the sum of the interior angles of each convex polygon.

a) nonagon b) 50-gon

~~the~me~a~su~re o~e~a c~n~e~o~

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

The measure of each exterior angle in a regular polygon is 24

°.

How many

sides does the polygon have?

Two interior angles of a pentagon measure 80

and 100

°.

The other three

angles are congruent. Find the measure of each of the three angles.

Name

Geometry

Interior Angles

Find the value for each variable.

/(2x-5o) o

150

2x+2 O) o

×÷40)

Find the measure

of each anc~le

z--

m~A~D =

,;~ZD~(2 =

4Z o

CDB :

mZHGE -

mLEGB

5z-10)

(5Z

+25)