1. Angles of Polygons
Find the sum of the measures of the interior angles of a
polygon
Find the sum of the measures of the exterior angles of a
This scallop resembles a 12-sided polygon with diagonals drawn from one of the vertices.

2. Quadrilateral SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Quadrilateral

3. Pentagon SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Pentagon

4. Hexagon SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Hexagon

5. Heptagon SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Heptagon

6. Octagon SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Octagon

7. Interior Angle Sum Theorem
If a convex polygon has n sides then the sum S of the measures of its interior angles is:
S = 180(n - 2)

8. EXAMPLE 1 N = 5 S = 180(n – 2) = 180(5 – 2) or 540
Find the sum of the interior angles of the pentagon.
N = 5
S = 180(n – 2)
= 180(5 – 2) or 540

9. Convex Polygons No. of sides n Name Angle Sum Sum ÷ n 3 triangle 180°
60° 4
quadrilateral
360°
90° 5
pentagon
540°
108° 6
hexagon
720°
120° 7
heptagon
900°
129° 8
octagon
1080°
135° 9
nonagon
1260°
140° 10
decagon
1440°
144°
What is the exterior angle of each regular polygon?
Is the total 360°in each case?

10. Interior Angles of Polygons
Find the unknown angles below. x
100° w
90°
75°
120°
120°
70°
75°
(5 – 2) x 180° = 540°
540 – =
(4 – 2) x 180° = 360°
360 – 245 = 115°
125o
130o
136o z
100o
125o
112o
136o
108o
122o y
134o
126o
(6 – 2) x 180° = 720°
720 – =
(7 – 2) x 180° =

11. Interior Angles of Polygons
Calculate the angle sum and interior angle of each of these regular polygons. 1 2 3 4
7 sides
9 sides
10 sides
11 sides
Septagon/Heptagon
Nonagon
Decagon
Hendecagon
900°/128.6° 5 6 7
12 sides
16 sides
20 sides
Dodecagon
Hexadecagon
Icosagon

12. EXAMPLE 2
Find the measure of each interior angle
n = 4 B C
2x°
2x°
Sum of interior angles is
180(4 – 2) or 360 x° x° A D

13. Exterior Angles of Polygons
Exterior Angle Theorem
The exterior angle of a triangle is equal to the sum of the remote interior angles.
remote interior angles A
exterior angle B C D
i.e. ACD = ABC + BAC

14. Exterior Angle Sum Theorem
If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° 2 1 3 5 4