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 = $\dfrac{{{{360}^ \circ }}}{n}$ , $n$ is the number of side
The regular octagon is a polygon with \[8\] Equal sides.
Substitute $n = 8$ into the formula $\dfrac{{{{360}^ \circ }}}{n}$.

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 = $\dfrac{{{{360}^ \circ }}}{n}$ , $n$ is the number of sides.
The number of sides of the octagon is $8$.
Substitute $n = 8$ into $\dfrac{{{{360}^ \circ }}}{n}$.
The size of exterior angle = $\dfrac{{{{360}^ \circ }}}{8}$
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 =\[\dfrac{{\left( {n - 2} \right)}}{n}{\text{ }} \times {\text{ }}{180^ \circ }\]
The exterior angle = $\dfrac{{{{360}^ \circ }}}{n}$ , $n$ is the number of side