Interior/Exterior Polygon Angles

Triangle

3 sides, 1 triangle, 180 degrees

sum of exterior angles of a polygon

360

number of sides of regular polygon

360 / one exterior

Quadrilateral

4 sides, 2 triangles, 360 degrees

Pentagon

5 sides, 3 triangles, 540 degrees

Hexagon

6 sides, 4 triangles, 720 degrees

Heptagon

7 sides, 5 triangles, 900 degrees

How to solve: what is the measure of each interior angle of a regular hexagon?

720/6=120

Octagon

8 sides, 6 triangles, 1080 degrees

Nonagon

9 sides, 7 triangles, 1260 degrees

Exterior Angles Sum

Always supplementary to their adjacent interior angle The sum of exterior angles of a polygon is 360

exterior angle of a regular polygon

always supplementary to adjacent interior

Interior angle of a regular polygon (all sides are equal)

sum of interior angles/# of sides

interior angle of regular polygon

sum of interior angles/# of sides

How to calculate total sum of interior angles of a polygon

# triangles*180

sum of interior angles of a polygon

#of trianlges* 180=sum of interior angles

How to calculate # of triangles in a polygon

#sides-2

How to solve: what is the sum of the measures of the interior angles of a 25-gon?

(n-2)180 (25-2)180= 4140

How to solve: if the interior of a regular polygon measures 1620 degrees, how many sides does the polygon have

(n-2)180=1620 180n-360=1620 n=11

Sum of interior angles formula

(n-2)180=s n is # of sides of a polygon s is the sum of the inside angles

Decagon

10 sides, 8 triangles, 1440 degrees