## 1-6 Angles & Polygons

**Objective:**To find angle measures of a polygon.

**CCSS Standard:**8.G.5

Two consecutive (in a row) sides of a polygon form an

To find the angle sum of the interior angles of any polygon use the formula

where "n" represents the number of sides in the polygon.

**interior angle**. This is an angle on the inside of the polygon.To find the angle sum of the interior angles of any polygon use the formula

**(n - 2)180**where "n" represents the number of sides in the polygon.

Here's how the above formula works:

Triangle, n=3 -- (3-2)180 = (1)180 = 180 degrees

Quadrilateral, n=4 -- (4-2)180 = (2)180 = 360 degrees

Pentagon, n=5 -- (5-2)180 = 3(180) = 540 degrees

Hexagon, n = 6 -- (6-2)180 = (4)180 = 720 degrees

What is the angle measure of a decagon?

Triangle, n=3 -- (3-2)180 = (1)180 = 180 degrees

Quadrilateral, n=4 -- (4-2)180 = (2)180 = 360 degrees

Pentagon, n=5 -- (5-2)180 = 3(180) = 540 degrees

Hexagon, n = 6 -- (6-2)180 = (4)180 = 720 degrees

What is the angle measure of a decagon?

An

**exterior angle**of a polygon is an angle formed by a side AND an extension of an adjacent side.

The measure of an exterior angle of a triangle is equal to the measure of the interior angles at the other two vertices. For example, the exterior angle above would equal angle A + angle B.