Question

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

Answer 1

Answer:

$x=45$°

Step-by-step 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:

$\frac{360}{n}$

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

$n=8$

so the value of x is:

$x=\frac{360}{n}\\ \\x=\frac{360}{8}\\ \\x=45$°

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