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Bell Ringer
2. Name all angles not adjacent to D.
3. Name the polygon.
1. Name all diagonals with an endpoint at vertex B.
2x + 2
The perimeter of the parallelogram is 84 feet. 4. Find the length of the base.
4x - 2
Polygon Interior Angles Theorem- the sum of the measures of the interior angles
of a polygon with n sides is (n – 2)(180°)
7 sides 10 sides 11 sides
12 sides 16 sides 20 sides
9 sides
Find the sum of the measures of the interior angles.
Polygon Exterior Angles Theorem- the sum of the measures of the exterior
angles, one at each vertex is 360°
Exterior Angles of Polygons
Interior Angles
Exterior Angles
?180o
Exterior angles of a polygon sum to 360o.
Exterior Angles of Polygons
Regular Polygons
Square
4
Pentagon
5
Hexagon
6
Octagon
8
Equilateral Triangle
3
360120
3
oo
120o
120o
120o
60o60o
60o
36090
4
oo
90o
90o
90o
90o
90o90o
90o 90o
36072
5
oo
72o
72o
72o
72o
72o
108o
108o
108o
108o
108o
36060
6
oo
60o
60o
60o
60o
60o
60o
Interior angles are 180 – 60 =
120o
36045
8
oo
Interior angles are 180 – 45 =
135o45o
45o
45o45o
45o
45o
45o
45o
Exterior Angles of Polygons
Septagon/Heptagon Decagon Hendecagon
Dodecagon Hexadecagon
Icosagon
7 sides 10 sides 11 sides
12 sides 16 sides 20 sides
9 sides
Nonagon
51.4o/128.6o 40o/140o 36o/144o 32.7o/147.3o
30o/150o 22.5o/157.5o 18o/162o
Calculate the exterior and interior angles of each of these regular polygons.
1 2 4
5 6 7
3
Angle w = 360 – (125 + 90) = 145o
1 2
3 4
88o
w115o
108o
x
80o
65o
y
125o
Diagrams not
accurately drawn
58o
z
32o
55o
70o45o
Calculate the value of the unknown angles.
Exterior Angles of Polygons
125o
Angle x = 360 – (108 + 88 + 115) = 49o
Angle y = 360 – (90 + 55 + 80 + 65) = 70o
Angle z = 360 – (32 + 70 + 55 + 45 + 122) = 36o
122o
?55o
?
You try! Diagrams not
accurately drawn
3 463o
73o
y
115o
58o
z
33o 55o
130o
45o
1 2 110o
w85o
110o
x
130o
What’s happened? (mathematically
speaking)
A hendecagon is laying eggsagons!
And finally:
