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• Measure of an Exterior Angle of a Regular Octagon

# Measure of an Exterior Angle of a Regular Octagon?

TopOctagon is a type of regular Polygon, whose all 8 sides are equal in nature. Now question arises how to measure of an exterior angle of a regular octagon? So, for evaluation of exterior angles of octagon we use following steps:
Step 1: For evaluation of exterior angle of octagon, first we calculate interior angles by using following formula:
Interior angle of polygon = 180 * (n – 2) / n, here ‘n’ is equal to number of side of polygon,
As we all know that octagon has 8 sides, so:
Interior angle of octagon = 180 * (8 – 2) / 8,
= 180 * 6 / 8,
= 1080 / 8,
= 135 degree.
So, interior angle of octagon is equal to ‘135 degree’.
Step 2: After evaluation of interior angle of octagon, now we calculate exterior angle of Hexagon by using following formula:
Exterior angle of polygon = 180 – interior angle of polygon,
As we all know that interior of octagon is equal to ‘135 degree’, so:
Exterior angle of octagon = 180 – interior angle of octagon,
= 180 – 135,
= 45 degree,
So, exterior angle of octagon is equal to ‘45 degree’.
Therefore, we use above two steps for evaluating an exterior angle of octagon and interior angle of octagon is equal to ‘135 degree’ and exterior angle of octagon is equal to ‘45 degree’.
Now we calculate sum of all exterior angles of an octagon by using following formula:
Sum of exterior angle = 180 * n – 180 * (n - 2),
Here n is equal to number of side of a polygon and as we all know that octagon has 8 side
= 180 * 8 – 180 * (8 – 2),
= 1440 – 1080,
= 360 degree,
So, sum of all exterior angle of an octagon is equal to ‘360 degree’.