Polygons You can determine how many degrees a geometric shape has by figuring out how many triangles you can make in the shape. Each triangle that fits within a shape has 180 degrees. Add the triangles together and you know how many degrees the shape has. For example, you can divide a square into two triangles. 180 degrees + 180 degrees = 360 degrees, the number of degrees in a square or any quadrilateral.



The following table shows how to determine the number of degrees in a shape using triangles. The last row shows the general formula for polygon degrees.

polygons	shape	# of sides	# of triangles	total degrees
Triangle		3	1	180
Quadrilateral		4	2	360
Pentagon		5	3	540
Hexagon		6	4	720
Heptagon		7	5	900
N-Gon	N sided shape	N	N-2	180*(N-2)

For the first table it is showing the number of sides and the name of the shape. To find the number of triangles in the shape take the number of sides minus 2. To find the total degrees in a shape you multiply 180 by the number of triangles in a shape, because the degrees in a triangle always add up to 180.

There is another trick for finding out the number of degrees in one angle of any polygon. This table will show you the pattern.

polygons	# of sides	total degrees	one angle
Triangle	3	180	60
Quadrilateral	4	360	90
Pentagon	5	540	108
Hexagon	6	720	120
Heptagon	7	900	128.57
N-Gon	N	180*(N-2)	180*(N-2)/N

The measure of one angle in a shape is the total degrees divided by the number of sides of the shape.

The final table shows the interior and exterior angle measures of a polygon. Interior angles are the angles inside the figure, exterior angles are outside of the shape, like this:

polygons	# of sides	exterior and interior angles	intereior angles	exterior angles
Triangle	3	540	180	360
Quadrilateral	4	720	360	360
Pentagon	5	900	540	360
Hexagon	6	1080	720	360
Hentagon	7	1260	900	360
N-Gon	N	180*N	(180*N)-360	360

The third table is showing the measure of interior angles and exterior angles. For exterior and interior angles you take the number of sides times 180. For just the interior angles you take 180 times the number of sides and then minus 360. The measurement of exterior angles will always be 360.