Question

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

Answer 1

Answer:

Exterior angle = 45°

Step-by-step 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:

$\frac{(n - 2) \times 180}{n} \\ \frac{(8 - 2) \times 180}{8}\\ \frac{6 \times 180}{8} \\ \frac{1080}{8}$ = 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

Answer 2

Answer:

The measure of one exterior angle is 45 degrees.

Step-by-step 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.