Question
Jessica is drawing a regular octagon.
What is the measure of one interior angle?
What is the measure of one interior angle?
Answers
GPT-4o mini
To find the measure of one interior angle of a regular octagon, we can use the formula for the measure of an interior angle of a regular polygon, which is given by:
\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]
where \( n \) is the number of sides of the polygon. For an octagon, \( n = 8 \).
Substituting \( n \) into the formula:
\[
\text{Interior Angle} = \frac{(8 - 2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8}
\]
Calculating this step-by-step:
1. Calculate \( 6 \times 180^\circ \):
\[
6 \times 180^\circ = 1080^\circ
\]
2. Divide by 8:
\[
\frac{1080^\circ}{8} = 135^\circ
\]
Therefore, the measure of one interior angle of a regular octagon is \( \boxed{135^\circ} \).
\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]
where \( n \) is the number of sides of the polygon. For an octagon, \( n = 8 \).
Substituting \( n \) into the formula:
\[
\text{Interior Angle} = \frac{(8 - 2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8}
\]
Calculating this step-by-step:
1. Calculate \( 6 \times 180^\circ \):
\[
6 \times 180^\circ = 1080^\circ
\]
2. Divide by 8:
\[
\frac{1080^\circ}{8} = 135^\circ
\]
Therefore, the measure of one interior angle of a regular octagon is \( \boxed{135^\circ} \).