If every internal angle of a polygon is at most 180 degrees, the polygon is called convex.
In contrast, an exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
To find the total measure of degrees in a regular polygon, (regular meaning all sides and angles are equal) you must take the number of sides the polygon has, n, subtract 2 from it, then multiply that number by 180°.
A decagon, a polygon with 10 sides, is a simple shape to figure the total measure of
Solution to the decagon:
The total measure of the decagon is 1440°.
Divide that number by the number of sides, in this case, 10, to find the measure of each angle.
Each interior angle of a regular decagon is 144°.
It is easier to use measure of an exterior angle. Since every regular polygon can be built from n isosceles triangles, to get the measure of an internal angle simply subtract measure of exterior angle (see below) from 180°
For decagon this gives us:
To find the measure of a regular decagon's exterior angles, divide 360° by the number of sides the polygon has, in this case, 10.
So all the exterior angles in a regular decagon are 36°.