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Q: What is the interior and the exterior angle of a regular polygon?

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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

The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.

It is a regular octagon which has 8 sides

If those are exterior angles, the exterior angles of any polygon add up to 360. That would be 18 sides.

Related questions

160

If the polygon has n sides, each exterior angle is 360/n degrees.The interior angle is 180 less exterior angle.

Exterior angle regular polygon = 360° ÷ number of sides = 360° ÷ W Interior angle regular polygon = 180° - exterior angle regular polygon = 180° - (360° ÷ number of sides ) = 180° - (360° ÷ W)

Interior angle: 135 degrees Exterior angle: 45 degrees

Interior angle = 120 degrees Exterior angle = 60 degrees

360 ________________________________________________ Sum of Interior Angles of a Polygon = 180 (n-2) Sum of Exterior Angles of a Polygon = 360 The sum of an angle and an exterior angle of a regular polygon is 360

180-interior angle = exterior angle If it's a regular polygon then: 360/number of sides = exterior angle

Exterior angle 12 degrees Interior angle 168 degrees

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180

180

A regular polygon of 30 sides will each have an exterior angle of 12 degrees and an interior angle of 168 degrees.

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