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°
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