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It is a plane (2-d) figure defined by N straight sides. An N-sided polygon is used to make statements which depend only on N and not any further details of the shape. For eaxmple, the interior angles of an N-sided polyogon add to (N-2)*180 degrees. This statement is true for all N greater than 2. It does not matter whether you are talking about a triangle, a quadrilateral, a pentagon, etc.
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How many diagonals are in a 7 sided polygon?
A 4-sided polygon has 2 diagonals. A 5-sided polygon, 5. 6-sided, 9. By induction, an n-sided polygon has 'n*(n-3)/2' diagonals. "n" is how many sides a shape has. so, (7)*(7-3)/2 now we have, 7*4/2 so, 28/2 = 14 Therefore, a 7-sided polygon would have 14 diagonals.
What is the measure in degrees of each central angle of a regular 15-sided polygon?
The central angle of a n-sided regular polygon = 360 degrees / n. Hence, the central angle of a 15-sided regular polygon = 360 degrees / 15 = 24 degrees ============================
Work out the exterior and interior angles of a regular polygon with 15 sides?
The sum of the exterior angles of a polygon is 360o, so for a regular n-sided polygon, each is 360o/n. The interior and exterior angles of a polygon are supplementary, that is sum to 180o. For a regular 15 sided polygon: exterior_angle = 360o / 15 = 24o interior_angle = 180o - exterior_angle = 180o - 24o = 156o Alternatively: The sum of the interior angles of a n-sided polygon is (n-2) x 180o, so for a regular n-sided polygon each interior angle is (n-2) x 180o / n. For a 15 sided polygon: interior_angle = (15 - 2) x 180o / 15 = 13 x 12o = 156o exterior_angle = 180o - interior_angle = 180o - 156o = 24o.
What is the sum of the interior angle of a sixteen sided polygon?
For an N-sided polygon, the sum of the interior angles is: N*(180° - 360°/N) or just N*180° - 360°. See related link. So for N=16, the sum is 2520°
What is the sum of angles in a 28-sided polygon?
The sum of the interior angles of a polygon with n sides is 180o × (n - 2), consequently the sum of the interior angles of a 28-sided polygon is 4680o (180o × 26).
