Here’s a pentagon, a 5-sided polygon. From vertex A we can draw two diagonals which separates the pentagon into three triangles. We multiply 3 times 180 degrees to find the sum of all the interior angles of a pentagon, which is 540 degrees.

Regular Polygons

In geometry, a hexagon (from Greek ἕξ, hex, meaning “six”, and γωνία, gonía, meaning “corner, angle”) is a six-sided polygon or 6-gon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

hexagon

There are six angles, so 720 ÷ 6 = 120°. Each interior angle of a regular hexagon has a measure of 120°. Because the sum of these angles will always be 360°, then each exterior angle would be 60° (360° ÷ 6 = 60°).

Lesson Summary An interior angle is located within the boundary of a polygon. The sum of all of the interior angles can be found using the formula S = (n – 2)*180. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides.

What about when you just want 1 interior angle? In order to find the measure of a single interior angle of a regular polygon (a polygon with sides of equal length and angles of equal measure) with n sides, we calculate the sum interior anglesor (n−2)⋅180 and then divide that sum by the number of sides or n.

In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon.

icosihexagon