What is the measure of each exterior angle of a regular octagon?

What is the measure of each exterior angle of a regular octagon?

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 75 degrees

Answer: (B)

To find the measure of each exterior angle of a regular octagon, you can use the formula for the measure of an exterior angle of a regular polygon, which is given by: \[ \text{Exterior angle} = \frac{360^\circ}{n} \] where \( n \) is the number of sides of the polygon. In the case of a regular octagon, there are 8 sides. Substituting 8 into the formula: \[ \text{Exterior angle} = \frac{360^\circ}{8} = 45^\circ \] This means that each exterior angle of a regular octagon measures 45 degrees. The reasoning behind this formula is that the sum of all exterior angles of any polygon is always 360 degrees, regardless of the number of sides. Each angle in a regular polygon is the same, so dividing the total of 360 degrees by the number of sides gives you the size of each individual exterior angle. In this scenario, since all the angles are equal in a regular octagon, the calculated measure accurately reflects the measure of each exterior angle, confirming that the correct answer is indeed 45 degrees.

To find the measure of each exterior angle of a regular octagon, you can use the formula for the measure of an exterior angle of a regular polygon, which is given by:

[

\text{Exterior angle} = \frac{360^\circ}{n}

]

where ( n ) is the number of sides of the polygon. In the case of a regular octagon, there are 8 sides.

Substituting 8 into the formula:

[

\text{Exterior angle} = \frac{360^\circ}{8} = 45^\circ

]

This means that each exterior angle of a regular octagon measures 45 degrees. The reasoning behind this formula is that the sum of all exterior angles of any polygon is always 360 degrees, regardless of the number of sides. Each angle in a regular polygon is the same, so dividing the total of 360 degrees by the number of sides gives you the size of each individual exterior angle.

In this scenario, since all the angles are equal in a regular octagon, the calculated measure accurately reflects the measure of each exterior angle, confirming that the correct answer is indeed 45 degrees.