Question

A regular hexagon and a regular octagon share a side. What is the measure of x, the angle between a side of the hexagon and a side of the octagon?

Answer 1

`x = 105^o`

Explanation:

It can be seen from the sketch that the angle x is the sum of the exterior angle of the hexagon and the exterior angle of the octagon.
The exterior angles of any regular polygon add up to `360^o`
The exterior angle of the octagon is `360/8 = 45^o`
The exterior angle of the hexagon is `360/6 = 60^o`
Therefore `x = 45 + 60 = 105^o`