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Each interior angle of an octagon is 135o.
The sum of the exterior angles of a polygon is 360o.
A regular octagon has equal angles, thus:
8 x exterior_angle = 360o
⇒ exterior_angle = 360o ÷ 8 = 45o
The interior and exterior angles of a polygon are supplementary, that is sum to 180o.
interior_angle + 45o = 180o
⇒ interior_angle = 180o - 45o = 135o.
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