3-5 THE POLYGON ANGLE-SUM THEOREMSSWBAT: • Classify polygons• Find the sums of the measures of the interior

and exterior angles of polygons

• Polygon: closed plane figure with at least 3 sides that are segments; the sides intersect only at their endpoints, and no adjacent sides are collinear

To name a polygon, start with any vertex and list the vertices consecutively in a clockwise or counterclockwise direction.

What are the different ways you can name this polygon?ABCDEEABCDDCBAEBCDEA and many more…

Diagonal: a segment that connects two nonconsecutive vertices

Name the diagonals below.a) b)

• You can classify a polygon by the number of sides it has. Here are some common polygon names:

• Polygons are classified as convex or concave.• A convex polygon has no diagonal with points outside the

polygon.

• A concave polygon has at least one diagonal with points outside the polygon.

Example 1: Classify each polygon by its sides. Identify each as convex or concave.

You try.c) d)

c) Octagon; concave

d) quadrilateral; convex

Polygon Angle Sum Theorem

Example 3: The sum of the measures of the angles of a given polygon is 720. How can you find the number of sides in the polygon?

Example 4

Try this.

Think about this one…Pentagon ABCDE has 5 congruent angles. Find the measure of each angle.

• This is the Sum of All Angles!• How many angles are there in

total?• How would we find one?

A little more terminology…

Find the measure of an exterior angle for a regular decagon.

You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of the exterior angles, one at each vertex, is 360.

• The sum of the exterior angles of any polygon is 360, so what polygon has its interior angles sum to 360?