A polygon is a closed figure with at least 3 straight sides and angles.

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​What is a polygon?

A polygon is named according to the number of sides it has.

*A circle is NOT a polygon because it does not have straight sides or angles.

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​Naming Polygons

​A regular polygon has equal side lengths and equal angle measures.

​REGULAR Polygons

Formulas we will use today.

This is the formula that you use to find out how many degrees are inside of a polygon.


The letter "n" gets replaced with the number of sides the polygon has.

Triangle = (3 - 2) x 180 = 180 degrees

Quadrilateral = (4 - 2) x 180 = 360 degrees

Decagon = (10 - 2) x 180 = 1440 degrees

Formula for the Sum of Interior Angles

This is the formula that you use to find out how many degrees one angle inside a polygon is.


The letter "n" gets replaced with the number of sides the polygon has.

Triangle = ((3 - 2) x 180)/3 = 60 degrees

Quadrilateral = ((4 - 2) x 180)/4 = 90 degrees

Decagon = ((10 - 2) x 180)/10 = 144 degrees

Formula for the Each Interior Angles

This is the formula that you use to find out how many degrees one angle outside a polygon is.


The letter "n" gets replaced with the number of sides the polygon has.

Triangle = 360/3 = 120 degrees

Quadrilateral = 360/4 = 90 degrees

Decagon = 360/10 = 36 degrees

Formula for the Each Exterior Angles

This is the answer to the sum of all exterior (outside) angles of a polygon.


Triangle = 360 degrees

Quadrilateral = 360 degrees

Decagon = 360 degrees

Answer to the Exterior Angle Sum