Question

Find the size of each exterior angle of a regular octagon.

Answer 1

Hint: In a regular polygon the sides are all the same length and the interior angles are all the same size.
In a regular polygon, the exterior angle = ${\displaystyle \frac{{360}^{\circ }}{n}}$ , $n$ is the number of side
The regular octagon is a polygon with $$8$$ Equal sides.
Substitute $n=8$ into the formula ${\displaystyle \frac{{360}^{\circ }}{n}}$.

Complete step-by-step answer:
In the regular: All sides equal and all angles equal.
The sum of the exterior angles of a polygon is ${360}^{\circ }$
The size of exterior angle = ${\displaystyle \frac{{360}^{\circ }}{n}}$ , $n$ is the number of sides.
The number of sides of the octagon is $8$.
Substitute $n=8$ into ${\displaystyle \frac{{360}^{\circ }}{n}}$.
The size of exterior angle = ${\displaystyle \frac{{360}^{\circ }}{8}}$
Each exterior angle =${45}^{\circ }$
In the regular, all angles are equal so the size of each angle is ${45}^{\circ }$.

Final Answer: The size of each exterior angle of a regular octagon.

Note:
The list of some common formula;
Interior Angle = $${180}^{\circ }$$ – Exterior Angle
Exterior Angle = $${180}^{\circ }$$ – Interior Angle
The interior angle =$${\displaystyle \frac{\left(n-2\right)}{n}}\times {180}^{\circ }$$
The exterior angle = ${\displaystyle \frac{{360}^{\circ }}{n}}$ , $n$ is the number of side