Polygon Angle Sum Packet PDF
Polygon Angle Sum Packet PDF
Polygon Angle Sum Packet PDF
Geometry Polygons
Use the given information to complete the table. Round to the nearest tenth if necessary.
Measure of ONE Exterior Angle Measure of ONE
Interior Angle INTERIOR Angle EXTERIOR Angle
# Sides
Sum Sum
(Regular Polygon) (Regular Polygon)
1)
2) 14
3) 24
4) 17
5) 1080°
6) 900o
7) 5040°
8) 1620°
9) 150°
lO) 120°
11) 156°
12) 10°
13) 7.2°
14) 90°
0
15)
Geometry NAME:
3) 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.
c) Find the number of sides in the polygon and the type of polygon.
5) Five angles of a hexagon have measures 100°, 110°, 120°, 130°, and 140°.
What is the measure of the sixth angle?
6) Find the value ofx.
a) b)
7) ABCDE and HIJKL are regular pentagons and AEFGHL is a regular hexagon.
If Z.ABK -=/LKB, find m/_ABK.
B K
4
Geometry NAME:
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
720°
For a hexagon: One interior angle = - 120°
6
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 OR 157.5n = (n-2)’180
What is the value of n?
2) Find the sum of the measures of the interior angles of a convex heptagon.
5) Can the interior angles of a polygon have a sum between 4300° and 4400°?
If so, how many sides can it have?
6) The measure of the interior angle of a regular polygon is 179°. How many sides does it
have?
7) Is it possible for a regular polygon to have each of its interior angles measure 142°?
Support your answer.
10o
11. 13,
- this doesn’t mean classify!!
Name the Polygon ~o different ways° Remember
14.
Matching:
16. lldOdecagon
17 ...... triangle
pentagon ~C. 5
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 ~
&
&
0
28. Explain why the given figure is not a polygon. Your answer must be in
a. odagon
b. pentagon
c. hexagon
d. heptagon
a. octagon
b. pentagon
a. odagon
b. pentagon
c, hexagon
d. decagon
a. octagon
b. pentagon
c. hexagon
d. decagon
Find the measure of the variables.
the measure of the variables.
Find the measure of/-i in each figure,
:/..3. ~
15.
16,
6x
Z1. 0 Z2.
310. Sketch a plane figure that is not a polygon and explain why it is not_.
~ 1. Sketch the following:
c) regular quadrilateral
Interior Exterior
a) nonagon b) 50-gon
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
~q
×÷40)
2x+2 O) o
z--
m~A~D = 4Z o
,;~ZD~(2 =
mZ CDB :
(5Z +25) o
mZHGE - ._
mLEGB - 5z-10)o E F