What should the angles of a polygon add up to

Example 3: Find the measure of each interior angle of a regular hexagon Figure 3. Method 1: Because the polygon is regular, all interior angles are equal, so you only need to find the interior angle sum and divide by the number of angles. Method 2: Because the polygon is regular and all its interior angles are equal, all its exterior angles are also equal.

Look at Figure 2. This means that. Previous Triangles. Next Special Quadrilaterals. At this point you are now facing the same direction you started with having turned through a full circle.

This is the same regardless of how many sides the polygon has. Marine Biology. Electrical Engineering. Computer Science. Medical Science. Writing Tutorials. Performing Arts. Visual Arts.

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Political Science. Welcome to Owlcation. Related Articles. By Rachel M Johnson. There are two types of angles in a polygon - the Interior angles and the Exterior Angles. Let us learn about the various methods used to calculate the sum of the interior angles and the sum of exterior angles of a polygon.

Polygons are classified into various categories depending upon their properties, the number of sides, and the measure of their angles. Based on the number of sides, polygons can be categorized as:. A regular polygon is a polygon in which all the angles and sides are equal.

There are 2 types of angles in a regular polygon:. The interior angles of a polygon are those angles that lie inside the polygon. Observe the interior angles A, B, and C in the following triangle. The interior angles in a regular polygon are always equal to each other. Another way to calculate the sum of the interior angles is by checking the number of triangles formed inside the polygon with the help of the diagonals. An exterior angle outside angle of any shape or regular polygon is the angle formed by one side and the extension of the adjacent side of that polygon.

Observe the e xterior angles shown i n the following polygon. This can be proved with the following steps:. Check out these interesting articles related to the Sum of Angles in a Polygon.