What is the degree measure of each interiorangle and exterior angle in a regular 18-

gon?

18-gon: polygon with 18 sides

regular: all angles are equal all sides are equal

Problem:

Process:

1. Need to know formula/pattern for total angle measures INSIDE polygons.

2. Need to know formula/pattern for total angle measures OUTSIDE polygons

3. Need to divide the total by 18

What I already know:

The total number of degrees in a 3-sided polygon (triangle) is 180

Linear pair = 180°

1. Divide the polygon into triangles and cut them out

2. Knowing what you already know about the angles in a triangle, determine the sum of the angles in the pentagon

3. Look for a patter or formula

Tips (Interior Angle Groups)

1. Determine the sum of the INTERIOR angles first

Tips (Exterior Angle Groups)

1. I think the total number of degrees INSIDE/OUTSIDE a pentagon is:

2. I think the rule for any polygon is:

3. Using this the rule the measure of each INTERIOR/EXTERIOR angle in an 18-gon is:

Polygons

Define vocabulary need to discuss polygons; find formulas for the sum of the interior and exterior angles in any polygon and use them to find angle measures in regular polygons

How is the sum of the interior angles of a polygon determined?

What is true about the sum of the exterior angles of any polygon?

Closed figures No curves Sides meet end point to end point

Polygons

Diagonal: a segment connecting two vertices in a polygon.

Types of Polygons

Convex: Concave: diagonals can go outside the polygon

Equiangular Polygon Equilateral Polygon

all angles are equal all sides are equal

Regular Polygon all sides & angles are equal in

measure.

Triangle: 3 sides

Quadrilateral: 4 sides

Pentagon: 5 sides

Hexagon: 6 sides

Heptagon: 7 sides

Octagon: 8 sides

Nonagon: 9 sides

Decagon: 10 sides

Undecagon: 11 sides

Dodecagon: 12 sides

Names of Polygons

1. Total of Interior Angles: 180n – 360

2. Total of Exterior Angles = 360°

Theorems

# of sides

Find the total sum of the interior angles in a…

1. Octagon

2. Heptagon

Practice

Find the measure of each angle in a REGULAR

3. Nonagon

4. Decagon

Practice

Find the missing angle in each figure1. 2.

Practice