In geometry, an internal angle (or interior angle) is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon. A simple polygon has exactly one internal angle per vertex.

If every internal angle of a polygon is at most 180 degrees, the polygon is called convex.

Sum of internal angles

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A regular n-gon has an internal angle(s) of $(1-\backslash frac\{2\}\{n\})180$ (or alternately, of $(n-2)\backslash frac\{180\}\{n\}$) degrees.

Alternately, the internal angle(s) of a regular n-gon is (n−2)π/n radians ( or (n−2)/(2n) turns).

The sum of the internal angles of a polygon on a Euclidean plane with n vertices (or equivalently, n sides) is $(n-2)180$ degrees. For example, the internal angles of any triangle (n = 3) sum to 180 degrees. Another example is a rectangle, whose four internal angles are each 90 degrees, for a total of 360 degrees, the same as any quadrilateral.

Transversals and parallel lines

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Internal angles may also refer to the angles within the two parallel lines which are intersected by a transversal.

External angle law

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The sum of the internal angle and external angle for any vertex on a shape is always equal to 180 degrees.

Elementary geometry | Angle