What is the size of the exterior angle of a regular octagon? [closed]

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Can't really remember the rules for exterior and interior angles and don't really know what a "regular octagon" is.

Any help is appreciated thanks!

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4 Answers

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A regular $n$-gon are polygons with each side and internal angle being the same (e.g., equilateral triangles for $n = 3$, squares for $n = 4$, etc.). Each one has an interior angle of $\frac{180(n-2)}{n}$ degrees (e.g., as shown in the Angles section of Wikipedia's "Regular polygon" article). Thus, for regular octagons, $n = 8$, so each interior angle is $\frac{180 \times 6}{8} = 135^{o}$, and thus each exterior angle is $180^{o} - 135^{o} = 45^{o}$.

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This diagram of a regular octagon should help:

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The sum of the angles of an $n$-gon is $180(n - 2)$. Plugging $n = 8$ here, we obtain $180 × 6 = 1080^\circ.$ Since the polygon is regular, an interior angle measures $\frac{1080}{8} = 135^\circ $. Since the exterior and interior angles of any polygon are supplementary, the exterior angle is then $180 - 135 = 45^\circ $

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The regular octegon is a polygon with $8$ Equal sides .The interior angle is $135$ degrees.

The complement of that which is $180-135=45$ degrees is considered as the exterior angle.

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