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