What are the interior angles of a regular octagon?

What are the interior angles of a regular octagon?

• A. 120 degrees
• B. 135 degrees
• C. 150 degrees
• D. 160 degrees

Answer: (B)

To find the measure of the interior angles of a regular octagon, you can use the formula for the measure of each interior angle of a regular polygon, which is given by: \[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \] where \( n \) is the number of sides in the polygon. For an octagon, \( n = 8 \): \[ \text{Interior Angle} = \frac{(8 - 2) \times 180}{8} = \frac{6 \times 180}{8} = \frac{1080}{8} = 135 \text{ degrees} \] This calculation shows that each interior angle of a regular octagon measures 135 degrees. Thus, option B is the correct choice because it accurately reflects this calculation. Each angle in a regular octagon is equal, which is a key characteristic of regular polygons, further supporting the correctness of this answer.

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

[

\text{Interior Angle} = \frac{(n - 2) \times 180}{n}

]

where ( n ) is the number of sides in the polygon. For an octagon, ( n = 8 ):

[

\text{Interior Angle} = \frac{(8 - 2) \times 180}{8} = \frac{6 \times 180}{8} = \frac{1080}{8} = 135 \text{ degrees}

]

This calculation shows that each interior angle of a regular octagon measures 135 degrees. Thus, option B is the correct choice because it accurately reflects this calculation. Each angle in a regular octagon is equal, which is a key characteristic of regular polygons, further supporting the correctness of this answer.