Respuesta :
Answer:
The exterior angle is 45°
Option b is correct.
Step-by-step explanation:
Given a stop sign is a shape of a regular octagon
we have to find the measure of each exterior angle.
Exterior angle of a regular polygon is supplementary to its interior angle.
Sum of all interior angles of N-sided regular polygon can be calculated as
[tex](N-2)\times 180\text{ ,where N ios number of sides }[/tex]
[tex](8-2)\times 180=1080^{\circ}[/tex]
Since it is a regular octagon, so each of the interior angles of octagon are equal that are
[tex]\text{Measure of each interior angle=}\frac{\text{sum of interior angle}}{\text{Number of sides}}=\frac{1080}{8}=135^{\circ}[/tex]
Each exterior angle is the supplementary angle to the interior angle
∴ Exterior angle is
[tex]180 - 135 = 45^{\circ}[/tex]
The exterior angle is 45°
Option b is correct.
