Objective: I will investigate the measures of the interior and exterior angles of polygons.

8-1 day 2Objective: I will investigate the measures

of the interior and exterior angles of polygons

Find the sum of the measures of the interior angles of each convex polygon

A. 32-gon B. 18-gon C. 19-gon

D. 27-gon E. 4y-gon F. 2x-gon

Use the formula (n-2)180 to find the SUM of the INTERIOR angles of a convex polygon

Find the measure of each interior angle

An exterior angle is formed when one side of the polygon is extended at each vertex.

Note: the measure of one interior plus one exterior always equals 180 degrees because they are a linear pair!!!

What is an exterior angle???

Investigating Polygons

Exterior Angle sum example

What is the measure of each exterior angle of a regular pentagon?

1. What is the measure of each exterior angle of a regular decagon?

2. What is the measure of each exterior angle of a regular octagon?

3. What is the measure of each exterior angle of a regular heptagon?

4. What is the measure of each exterior angle of a regular 18-gon?

So… if the exterior angles always have a sum of 360 degrees try to answer these questions.

If each exterior angle of a regular polygon has a measure of 45 degrees. How many sides does the polygon have?

If each exterior angle of a regular polygon has a measure of 15 degrees. How many sides does the polygon have?

If each exterior angle of a regular polygon has a measure of 20 degrees. How many sides does the polygon have?

If each exterior angle of a regular polygon has a measure of 36 degrees. How many sides does the polygon have?

If an interior angle of a regular polygon has a measure of 157.5 degrees, how many sides does the polygon have?

If an interior angle of a regular polygon has a measure of 135 degrees, how many sides does the polygon have?

If an interior angle of a regular polygon has a measure of 60 degrees, how many sides does the polygon have?

If an interior angle of a regular polygon has a measure of 144 degrees, how many sides does the polygon have?

*** remember that one interior plus one exterior = 180

Homework: practice worksheet