Warm Up

1.A three sided polygon is called a __________.

2.A four sided polygon is called a ___________.

3.A five sided polygon is called a ___________.

4.The angles in a three sided polygon add up to ________ degrees.

5.The angles in a four sided polygon add up to ________ degrees.

Interior and Exterior Angles

To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals from one vertex of the polygon.

Convex Polygon

Number of Sides

Number of Triangles

Sum of the interior angles

In a regular polygon, the measure of EACH interior angle is:

Sum of the anglesNumber of angles

1. Find the sum of the interior angle measures of a convex heptagon.

2. Find the sum of the interior angle measures of a convex 15-gon.

3. Find the measure of each interior angle of a regular 16-gon.

4. Find the measure of each interior angle of a regular decagon.

5. Find the measure of each interior angle of pentagon ABCDE.

“y” is called an Exterior Angle.

An exterior angle plus it’s adjacent interior angle adds up to 180 degrees.All exterior angles in a any polygon adds up to 360 degrees.

Find the measure of an interior and exterior angle for each regular polygon. 1) 72-gon 2) 18-gon

3) 30-gon 4) octagon

5) pentagon 6) dodecagon

The measure of an exterior angle is given. Name the regular polygon it belongs to. 1) 120 " 2) 60 "

3) 7.2 " 4) 14.4 "

5) 18 " 6) 72 "

Find the name of the polygon with: 1) interior angles that sum to 180 ".

2) exterior angles that are 45 " each.

3) interior angles that are each 108 ".

4) interior angles that are each 150 ".

If each exterior angles of a regular polygon measures 36 ", find the sum of the measures of the interior angles.

If each exterior angles of a regular polygon measures 60 ", find the sum of the measures of the interior angles.

The sum of the measures of five interior angles of a hexagon is 525 degrees. 1) Find the measure of the 6th angle.

2) Would this be a regular hexagon?

The measure of an exterior angle of a regular octagon is (x+7). Find x and the measure of each angle in the octagon.

The sum of the measures of 8 interior angles of a nonagon is 1,110 degrees. Find the measure of the 9th angle.

Lesson Quiz

1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex.

2. Find the sum of the interior angle measures of a convex 11-gon.

3. Find the measure of each interior angle of a regular 18-gon.

4. Find the measure of each exterior angle of a regular 15-gon.