Answer:
[tex]x=45[/tex]°
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:
[tex]360[/tex]°
And to find the measure of a single external angle (such as the angle [tex]x[/tex] shown in the figure) we must divide 360 ° by the number of sides n:
[tex]\frac{360}{n}[/tex]
and for the regular octagon, since it has 8 sides:
[tex]n=8[/tex]
so the value of x is:
[tex]x=\frac{360}{n}\\ \\x=\frac{360}{8}\\ \\x=45[/tex]°
the measure of angle x is 45° which is the second option
