1. 6.1: Polygon Angle Theorems
Objectives
Find and use the measures of interior and exterior angles of polygons.
Handbook p. 19

2. Sum of Interior  Measures
Polygon Angle Sum Theorem:
The sum of the interior angles of a convex polygon is (n  2) 180.
Draw each diagonal from a single vertex, then complete the chart.
Polygon
# of Sides
# of Triangles
Sum of Interior  Measures
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon

3. 6.1: Polygon Angle Theorems
1. Find the sum of the interior angle measures of a convex heptagon.
(n – 2)180°
(7 – 2)180°
900°

4. 6.1: Polygon Angle Theorems
2. Find the measure of each interior angle of a regular 16-gon.
Step 1: Find the sum of the interior angle measures.
(n – 2)180°
(16 – 2)180° = 2520°
Step 2: Find the measure of one interior angle.

5. Handbook page 19 Interior Angles Exterior Angles Sum of all angles
Measure of one if the polygon is REGULAR!

6. 6.1: Polygon Angle Theorems
3. Find the measure of each interior angle of pentagon ABCDE.
(5 – 2)180° = 540°
35c + 18c + 32c + 32c + 18c = 540
135c = 540
c = 4
mA = 35(4°) = 140°
mB = mE = 18(4°) = 72°
mC = mD = 32(4°) = 128°

7. 6.1: Polygon Angle Theorems
4a. What is the measure of each interior angle of a regular decagon?
b. What is the measure of each exterior angle of a regular decagon?
c. What is the SUM of all of the exterior angles?

8. 6.1: Polygon Angle Theorems
In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.

9. 5. Find the measure of each exterior angle of a regular 20-gon.
A 20-gon has 20 sides and 20 vertices.
Sum of ext. s = 360°.
Measure of one ext.  =
The measure of each exterior angle of a regular 20-gon is 18°.

10. Angle measures of a convex polygon with n sides
Interior Angles
Exterior Angles
Sum of all angles
Measure of one if the polygon is REGULAR!

11. 6. Find the value of b in polygon FGHJKL.
15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360°
120b = 360
b = 3

12. 7. Name the convex polygon whose sum of its interior angle measures is 6840.
8. The exterior angle of a regular polygon is about 27.7. Find the number of its sides and the measure of each interior angle.