Internal angle

In geometry, an interior angle (or internal 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.

In contrast, an exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended from that side.

Interior angle measures of regular polygons

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°.

Example:

A decagon, a polygon with 10 sides, is a simple shape to figure the total measure of

Failed to parse (Missing texvc executable; please see math/README to configure.): (n-2) \times 180^\circ \!

= measure in degrees, when n = number of sides

Solution to the decagon:

Failed to parse (Missing texvc executable; please see math/README to configure.): (10-2) \times 180^\circ =1440^\circ. \!

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°.

Finding the exterior angles on a regular polygon

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.

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{360^\circ}{10} = 36^\circ.

So all the exterior angles in a regular decagon are 36°.

External links

• Internal angles of a triangle and External angles of a triangle With interactive animation
• Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference

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