Question

A graph artist was painting a logo in the shape of a regular polygon. She measured one of the exterior angle to be 45 degrees. How many sides does this polygon has? What is the name of such polygon?

Answer 1

We are given a polygon

with exterior angle= 45

sides=?

since the polygon exterior angle is 45

the interior angle is

$180-45=135$

the only polygon with inner angles equals to 135 is a octagon

other way to find the octagon is as we know that all the exterior angles sum to 360

then

$\frac{360}{45}$$\frac{360}{45}=8$