Page 1 of 3
Name
Date
Module #1:
Worksheet 5a:
Angles of Polygons
View Tutorial 5a
³Objective: Recognize and name convex polygons and regular polygons and
find the sum of the measures of interior and exterior angles of polygons.
Polygons
have vertices, sides, angles, and exterior angles.
A
Polygons are named by listing consecutive vertices in
order. ABCDEF is one name for this polygon.
F
A segment connecting two nonconsecutive vertices of a
polygon is called a diagonal. AD and FB are diagonals.
Convex polygons are polygons such that no part of a
diagonal is exterior to the polygon.
Exterior angleÆ
B
C
D
E
Not polygons
Convex polygons
Non-convex polygons
When we talk about polygons in this exercise, we will always mean convex polygons.
Polygons are classified according to the number of sides they have. Some of the special names
for polygons are given.
Number
3
4
5
6
7
8
9
10
of sides
Name of
polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon
n
n-gon
The sum of the measures of the interior angles of a convex
polygon with n sides is (n – 2) 180.
The sum of the measures of the exterior angles of any convex polygon,
one at each vertex, is 360.
See hexagon ABCDEF above for a diagram of an exterior angle.
Note that the sum of the exterior angles refers to each side being extended at each vertex,
all in the same direction.
Copyright 2000. All rights reserved.
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Page 2 of 3
Name
Date
Module #1:
Worksheet 5a:
Angles of Polygons
Example 1
A polygon has 24 sides (24-gon). Find:
a. the interior angle sum
b. the exterior angle sum
Solution
a. n = 24, so the sum of the interior
angles is:
(24 – 2)180 = 3960.
b. The sum of the exterior angles is 360.
For each polygon, find (a) the interior angle sum and (b) the exterior angle sum:
1. quadrilateral
a.
b.
2. 12-gon
a.
b.
3. hexagon
4. nonagon
a.
b.
5. decagon
a.
b.
6. pentagon a.
b.
7. octagon
a.
b.
8. 18-gon
a.
b.
9.
Copyright 2000. All rights reserved.
a.
b.
heptagon a.
b.
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Page 3 of 3
Name
Date
Module #1:
Worksheet 5a:
Angles of Polygons
Example 2
Find the value of x.
120°
Since this is a six sided figure, it is a hexagon.
Therefore, the sum of the interior angles is
(6 – 2)180 = 720°.
The sum of the angles shown is 4(120) = 480°.
So 720° - 480° = 240°.
The sum of the two missing angles must be 240°.
120°
x°
x°
120°
x + x = 240
2x = 240
2x = 240
2
2
x = 120°
120°
Find the value of x:
10.
x°
11.
150° 160°
150°
2x° 2x°
150°
150°
150°
150°
15.
16.
150°
65°
2.5x°
13.
120°
140°
x°
x°
60°
50° 150°
14.
12.
160°
60°
60°
3x°
3x°
x°
x°
17.
x°
95° 95°
65°
2.5x°
2x° 2x°
105° 105°
5x°
5x°
95° 95°
Copyright 2000. All rights reserved.
83