Question
What is the measure of each interior angle in a regular octagon?
The sum of a octagon =
°
Measure of 1 angle =
The sum of a octagon =
°
Measure of 1 angle =
Answers
GPT-4o mini
To find the measure of each interior angle in a regular octagon, we first need to calculate the sum of the interior angles of an octagon.
The formula for the sum of the interior angles of a polygon is:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides. For an octagon, \( n = 8 \).
Plugging that into the formula:
\[
\text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ
\]
Now, to find the measure of each interior angle in a regular octagon, we divide the sum of the interior angles by the number of angles (which is the same as the number of sides):
\[
\text{Measure of 1 angle} = \frac{\text{Sum of interior angles}}{n} = \frac{1080^\circ}{8} = 135^\circ
\]
So, the final answers are:
The sum of an octagon = **1080°**
Measure of 1 angle = **135°**
The formula for the sum of the interior angles of a polygon is:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides. For an octagon, \( n = 8 \).
Plugging that into the formula:
\[
\text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ
\]
Now, to find the measure of each interior angle in a regular octagon, we divide the sum of the interior angles by the number of angles (which is the same as the number of sides):
\[
\text{Measure of 1 angle} = \frac{\text{Sum of interior angles}}{n} = \frac{1080^\circ}{8} = 135^\circ
\]
So, the final answers are:
The sum of an octagon = **1080°**
Measure of 1 angle = **135°**