Question

A regular convex polygon has eight sides. What is the measure of an exterior angle?

Answer 1

The measure of one exterior angle is 45 degrees.

Explanation:

The formula to find exterior angle of and shape is 360 degrees divided by n (number of sides the shape has). 360 divided by 8 = 45 degrees.

Answer 2

Exterior angle = 45°

Explanation:

We know that the sum of exterior angles of a polygon is 360 degrees.

Since here we a regular polygon with eight sides (which makes it an octagon) so this means that the interior angles each would be equal to:

`((n - 2) * 180)/(n) \\ ((8 - 2) * 180)/(8)\\ (6 * 180)/(8) \\ (1080)/(8)` = 135 degrees

We know that each interior angle is supplementary to the exterior angle at the vertex.

So each exterior angle =
`180-135` = 45 degrees