Sum of Angles in Polygons

A polygon is a two-dimensional (flat) shape that has all straight lines. It needs to be closed, meaning there is an inside and outside.

Examples of polygons:

Things that are not polygons:

In order to determine the sum of the angles in any shape, we can divide it into triangles and then add all of those together to find the total.

However, this does not work if our triangles meet in the middle and create new angles that were not there before.

In this picture, new angles were created in the middle which is why it seems like there are 180° when the outside shape only has 360°

Name # of sides # of triangles Calculation Total sum of angles

Triangle 3 1 180° 180°

Quadrilateral 4 2 180° x 2 360°

Pentagon 5 3 180° x 3 540°

Hexagon 6 4 180° x 4 720°

Heptagon 7 5 180° x 5 900°

Octagon 8 6 180° x 6 1080°

Without drawing a picture, how many degrees do the angles in a nonagon (9 sides) add up to?

The angles in a nonagon (9 sides) add up to _____.

Without drawing a picture, how many degrees do the angles in a decagon (10 sides) add up to?

The angles in a decagon (10 sides) add up to _____.

Without drawing a picture, how many degrees do the angles in a nonagon (9 sides) add up to?

The angles in a nonagon (9 sides) add up to 1260°.

Without drawing a picture, how many degrees do the angles in a decagon (10 sides) add up to?

The angles in a decagon (10 sides) add up to 1440°.

Formula for total number of degrees in a polygon:

total degrees = (n – 2) x 180°, where n is the number of sides

this is how many this is how many degrees triangles there are each triangle is (two fewer than the number of sides)

Direct Station We will continue in our notes.

We will look at how to find single angles in polygons now that we know the formula for the total number of angles.

Independent Station

You are going to use one of the Pearson interactives in order to learn about the relationship between angles and sides in triangles.

You will need to open up the Google Form and Pearson at the same time and switch back and forth. The directions/questions are on the Google Form but you will need to use the Pearson interactive to help answer them.