Question

Given the regular octagon shown below, what is the measure of angle x?

Answer 1

`x=45`°

Explanation:

The angle shown in the figure is known as an external angle.

Also, in a regular polygon (like the regular octagon) the sum of all the exterior angles is the same regardless of the number of sides of the figure:

`360`°

And to find the measure of a single external angle (such as the angle
`x` shown in the figure) we must divide 360 ° by the number of sides n:

`(360)/(n)`

and for the regular octagon, since it has 8 sides:

`n=8`

so the value of x is:

`x=(360)/(n)\\ \\x=(360)/(8)\\ \\x=45`°

the measure of angle x is 45° which is the second option