Download 6-1: Polygon Angle

Shapes for the next page. Draw all the diagonals possible from only one
vertex. Use the information in the chart on the next page.
CP Geometry
Find the measures of the interior angles of the following
polygons. Complete the table below. Use the shapes on the
previous page.
Sum of Interior
Angle Measures
Polygon
# of Sides
# of s Formed
Quadrilateral
4
2
2*180=360
Pentagon
5
3
3*180=540
Hexagon
6
4
4*180=720
Heptagon
7
5
5*180=900
Octagon
8
6
6*180=1080
Polygon Angle-Sum Theorem
 The sum of the measures of the interior angles of an n-gon
is:
 n  2 180
Examples:
Find the sum of the measures of the following polygons:
a). Decagon
b). 15-gon
c). dodecagon
Complete Got It? #1 p. 353
Find the value of x in each polygon.
V
122°
U 121°
117°
T
10  2 180  8*180  1440
15  2 180  13*180  2340
12  2 180  10*180  1800
a. 2700
b. 1980 ÷ 180 + 2 = 13 sides
Types of Polygons
W
x°
120  118  117  121  122  mW  720
598  mW  720
mW  122
120° R
118°
S
86  118  129  82  mR  540
415  mR  540
mR  125
Equilateral Polygon
Q
82°
P 129°
T
x°
R
Equiangular Polygon
Regular Polygon
Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is:
118°
 n  2 180
86°
S
n
Complete Got It? #2 p. 354
9 − 2 180
7 180
=
= 140°
9
9
1
Exterior Angles of a Polygon
Polygon Exterior Angle Sum Theorem
Find the sum of the exterior angles, one from each
vertex of the following polygons.
90°
90°
86°
94°
1
75°
16°
164°
86  110  164  360
polygon, one at each vertex, is 360°.
m1  m2  m3  m4  m5  360
2
115°
65°
110° 70°
 The sum of the measures of the exterior angles of a
100°
80°
3
5
90  115  80  75  360
4
Complete Got It? #4 p. 355
360
= 40°
9
Homework: p. 356 #18-25, 29-36, 41
2