A polygon is a figure on the plane consisting of three or more sides that intersect at three or more points.
A polygon is said to be convex if each of its angles is less than 180 ?.
Usually polygons are considered as convex polygons.
To find the angles of a polygon, you need to have the minimum necessary set of initial data.
Let the lengths of all its sides be known for a polygon.
A polygon is said to be regular if its sides are equal to each other, and all angles are equal to each other.
If it is known in advance that the polygon is right, then the angles can be calculated from the formula
?? = 180? * (N - 2) / n, where n is the number of sides of the polygon.
For example, in the case of a regular octagon
?? = 180? * (8 - 2) / 8 = 135?
For an irregular triangle with known sides, the angles can be calculated by the cosine theorem, for example, for the angle ?? In the above figure, the formula takes the form
Cos ?? = (B? + C? - a?) / 2 • b • c
To find the angles of irregular polygons with a number of sides greater than 3, the presence of side lengths is not sufficient.