The measure of each angle of a regular octagon is ____.

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Detailed Solution

The measure of each angle of a regular octagon is

.
We have following formulas:
Sum of all interior angles can be calculated by

n − 2 × 180 °

.
Measure of each interior angle of n-sided polygon

= s u m o f a l l int e r i o r a n g l e s n

.
Where n is the number of sides.
Here n = 8.
Finding the sum of all interior angles:

= n − 2 × 180 ° = 8 − 2 × 180 ° = 6 × 180 ° = 1080 °

Finding measure of each interior angle of n-sides polygon:

= s u m o f a l l int e r i o r a n g l e s n = 1080 ° 8 = 135 °

Therefore, the correct answer is

135 °

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