1. Section 6.2
Angles of Polygons

2. Theorems Thm 6.1: Polygon Interior Angles Thm Corollary to Thm 6.1
The sum of the measures of the interior angles of a convex n-gon is (n-2) 180°
Corollary to Thm 6.1
The measure of each interior angle of a regular n- gon is
(n-2)180 n
n for all of these is the number of sides.

3. Find the measure of each interior angle of a regular pentagon:
(5-2)180°
3(180)=540°
540/5= 108°

4. More Thms cont. Thm 6.2 Polygon Exterior Angles Thm:
The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360°
Corollary to Thm 6.2:
The measure of each exterior angle of a regualr n-gon is (360°)/n

5. Examples:
1. One exterior angle of a regular convex polygon is 45°. What type of polygon is this?
45= 360/n
45n = 360
n= 8 so octagon
2. One exterior angle of a regular convex polygon is 30 °. What is the sum of the interior angles?
30n = 360
N = 12
(12- 2)180= 1800°

6. More exs.
3. Each interior angle of a regular convex polygon is 60°. How many sides does it have?
120n= 360
n= 3
4. What is the measure of each interior angle of a regular convex pentagon?
5n = 360
N = 72
180 – 72= 108
5. What is the measure of each interior angle of a regular convex nonagon?
140° 60

7. More exs.
A polygon has 27 sides, all diagonals are drawn from one vertex, how many diagonals are there?
5 sides
3 triangles
2 diagonals
6 sides
4 triangles
3 diagonals 24
N= sides
N -2 = # triangles
N- 3 = # of diagonals
Do it for an octagon
N = 8, triangles=6, diagonals= 5