7.3 Angles in Polygons

A Polygon is any closed shape.

 

The total interior angles of a polygon can vary.

 

With every side you add to a polygon, the total interior angles increases by 180°.

 

Total Interior Angles of Polygons

 

Starting with the smallest polygon - a triangle. A triangle's total interior angle is 180°.

 

Square/Rectangle = 360°

Pentagon = 540°

Hexagon = 720°

Heptagon = 900°

 

Notice the increase of 180° every time you add one side.

 

The equasion to find the total interior angles is:

 

Total Interior Angle = 180(n-2)

 

Where n represents the number of sides.

 

If you want to find the measurement of each individual angle, given the number of sides, the following equation is used.

 

Number of Sides = 180(n-2)/n

 

Where n represents the number of sides.

 

When the total interior angles is provided, you can use algebra to find the answer.

 

Example using total interior angles as 180°.

 

Total Interior Angle = 180(n-2)

180  = 180(n-2)

180  = 180n - 360        // Using Distributive Property

180+360  = 180n - 360 +360

540/180  = 180n/180

3  =  n

 

Therefore this shape has a total of 3 sides.

 

Number of Diagonal Lines from a Vertex

 

The equation to find the number of diagonal lines from a vertex is:

 

n-3

 

Where n represents the number of sides.

 

Number of triangles in a polygon

 

The equation to find the number of triangles in a polygon is:

 

n-2

 

Where n represents the number of sides.