By how many degrees does the measure of an interior angle of a regular octagon exceed the measure of an interior angle of a regular hexagon?
15
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To find the answer, we need to know the formula for calculating the measure of an interior angle of both a regular octagon and a regular hexagon.
The formula to calculate the measure of an interior angle of a regular polygon is given by:
Interior angle = (n-2) * 180 / n
Where n represents the number of sides of the polygon.
For a regular octagon (8 sides):
Interior angle of the octagon = (8 - 2) * 180 / 8 = 6 * 180 / 8 = 135 degrees
For a regular hexagon (6 sides):
Interior angle of the hexagon = (6 - 2) * 180 / 6 = 4 * 180 / 6 = 120 degrees
Now, to find by how many degrees the measure of an interior angle of a regular octagon exceeds the measure of an interior angle of a regular hexagon, we subtract the measure of the interior angle of the hexagon from the measure of the interior angle of the octagon:
135 degrees - 120 degrees = 15 degrees
Therefore, the measure of an interior angle of a regular octagon exceeds the measure of an interior angle of a regular hexagon by 15 degrees.