Q:

# How many degrees are in an octagon?

A:

There are a total of 1,080 degrees in the interior of an octagon. The angles can be evenly divided into eight angles of 135 degrees, as in a regular octagon, or any random combination in an irregular octagon.

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Credit: fdecomite CC-BY 2.0

An octagon is any closed two dimensional shape with eight sides. To determine the sum of the interior angles, as many triangles as needed to completely fill the inside of the shape should be created. The triangles should be oriented so that all triangle angles coincide with at least part of an octagon angle. As there are 180 degrees in a triangle, multiplying the number of triangles needed to fill the octagon in this manner, in this case six, by 180 degrees yields the total interior degrees of an octagon: 1,080.

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## Related Questions

• A:

An octagon has eight vertices. An octagon is a shape with eight sides, which makes eight angles and, therefore, eight vertices.

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• A:

An octagon is a shape most people can recognize right away; it has eight equal length sides and eight equal angles. You need a ruler, a protractor, a pencil and a piece of paper to construct an octagon.

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• A:

To draw an octagon to scale, first determine how big the octagon is to be. Draw the top line of the octagon to the desired length using a ruler. Use a protractor to determine a 135-degree angle from the end of the top line, and then use the ruler to draw a line the same length as the first at that angle. Repeat the process for all eight sides of the octagon.