Providing that it's a regular polygon then each interior angle measures 156 degrees
Example: a regular 15-gon The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. 180 x 13 = 2340 There are fifteen angles. 2340/15 = 156 An interior angle of a regular 15-gon is 156 degrees. There are two ways to find the exterior angles. The interior and exterior angles add up to 180. 180 - 156 = 24. The exterior angles of any polygon add up to 360. 360/15 = 24
If the 15-gon is a regular polygon, then: Sum of the interior angles = 180°(n - 2) = 180°(15 - 2) = 2,340° Each interior angle = 2340° ÷15 = 156°
Assuming that this is a regular pentadecagon, the 360° of the exterior offset angles are spread evenly, so are 24° each. This means the interior angles are 180-24=156°
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 ============================
It is 2340/15 = 156 degrees
Exterior: 24 degrees Interior: 156 degrees
Each exterior angle measures 24 degrees. Each interior angle measures 156 degrees
The exterior angle of an n-sided polygon is 360/n degrees. In this case n = 15 so angle is 24o
An interior angle of a 15-gon can have any measure between 0 and 360 degrees (excluding the two end values). The magnitude of an angle can only be determined theoretically (as opposed to measuring it) if it is a REGULAR polygon. The sum of the interior angles of a polygon (regular or not) with n sides can be shown to be (n-2)*180 degrees. For a 15-gon this would mean (15-2)*180 = 13*180 = 2340 degrees. If the polygon is regular, then each of the 15 angles is equal to 2340/15 = 156 degrees.
Providing that it's a regular polygon then each interior angle measures 156 degrees
15 degrees
the formula for an n-sided polygon to find it's interior angle is (n-2)180/n so the answer is 156 degree's.
360/15 = 24 degrees.
Each triangle has an angle sum of 180 degrees, so the sum of the interior angles of the 15-gon must be 13 × 180 = 2340 degrees.
Each interior angle is 156 degreesEach exterior angle is 24 degrees
24 degrees providing that it is a regular polygon. (And since each interior angle is 156 deg, it IS a regular 15-gon.) 360/15 = 24 degrees