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What is the measure of each exterior angle of a regular octagon?
30°
60°
45°
80°
45°
Remember the sum of all exterior angles for any polygon is always 360°. Simply divide 360 by the number of sides n to get the value for one exterior angle.
A regular octagon has n = 8 sides.
\text{Exterior Angle} = \frac{360°{n}
Remember the sum of all exterior angles for any polygon is always 360°. Simply divide 360 by the number of sides n to get the value for one exterior angle.
Many students confuse the interior angle formula \frac{(n-2) \times 180°{n} with the exterior angle formula, or mistakenly try to calculate the interior angle first and subtract from 180°.
Identify number of sides
A regular octagon is a polygon with n=8 equal sides and equal interior angles.
n=8
Apply exterior angle formula
The sum of exterior angles of any convex polygon is 360°. For a regular polygon, each exterior angle is equal.
\text{Exterior Angle} = \frac{360°{8}
Final calculation
Performing the division 360÷8=45.
45°
C is correct because the exterior angle of a regular octagon is calculated as 360°/8=45°.
The sum of the interior angle and exterior angle at any vertex of a polygon is always 180° (linear pair). Knowing this allows you to find one if the other is provided.
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