Question
How do you measure the vertex angle of a regular octagon?
Answers
GPT-4o mini
To measure the vertex angle of a regular octagon, you can use the formula for the interior angle of a regular polygon. The interior angle \( A \) of a regular polygon can be calculated using the following formula:
\[
A = \frac{(n - 2) \times 180^\circ}{n}
\]
where \( n \) is the number of sides of the polygon.
For a regular octagon, \( n = 8 \). Substituting this value into the formula gives:
\[
A = \frac{(8 - 2) \times 180^\circ}{8}
\]
Calculating this step-by-step:
1. Subtract 2 from 8:
\[
8 - 2 = 6
\]
2. Multiply 6 by 180 degrees:
\[
6 \times 180^\circ = 1080^\circ
\]
3. Divide 1080 degrees by 8:
\[
\frac{1080^\circ}{8} = 135^\circ
\]
Therefore, the vertex angle of a regular octagon is \( 135^\circ \).
\[
A = \frac{(n - 2) \times 180^\circ}{n}
\]
where \( n \) is the number of sides of the polygon.
For a regular octagon, \( n = 8 \). Substituting this value into the formula gives:
\[
A = \frac{(8 - 2) \times 180^\circ}{8}
\]
Calculating this step-by-step:
1. Subtract 2 from 8:
\[
8 - 2 = 6
\]
2. Multiply 6 by 180 degrees:
\[
6 \times 180^\circ = 1080^\circ
\]
3. Divide 1080 degrees by 8:
\[
\frac{1080^\circ}{8} = 135^\circ
\]
Therefore, the vertex angle of a regular octagon is \( 135^\circ \).