Each exterior angle = 360/number of vertices = 360/9 = 40 degrees.Each interior angle = 180 - exterior angle = 180 - 40 = 140 degrees.
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Each exterior angle: 40 degrees Each interior angle: 140 degrees
360 /each exterior angle
144o. Sum of exterior angles of a polygon is 360o. Each exterior angle for a regular decagon is 360o / 10 = 36o. Exterior and interior angles are supplementary, that is sum to 180o. Therefore the interior angle of a regular decagon is 180o - 36o = 144o.
180-interior angle = exterior angle 360/exterior angle = number of sides
If the interior angle = 140 degrees, then the exterior angle = 180 degrees - 140 degrees = 40 degrees. So the number of sides is 360 degrees / 40 degrees = 9 sides (a nonagon).