If one interior angle is 165 degrees, find the number of sides of the polygon.
It cannot be a regular polygon with interior angles of 24 degrees since the smallest interior angle in a regular polygon is 60 degrees. If it is an irregular polygon, then any one of them, with 3 or more sides, can have an angle of 24 degrees.
interior angle of an n-sided polygon = (180(n-2)/n)°interior angle of a 24-sided polygon = (180x22/24)° = 165°
180(n-2)/n 180(24-2)/24 180(22)/24 3,960/24 165 Thus, each angle in a regular polygon that has twenty four sides is 165 degrees, and the sum of all the angles is 3,960 degrees.
15 sides
Interior angle 156 degrees Exterior angle 24 degrees 360/24 = 15 sides
If one interior angle is 165 degrees, find the number of sides of the polygon.
It cannot be a regular polygon with interior angles of 24 degrees since the smallest interior angle in a regular polygon is 60 degrees. If it is an irregular polygon, then any one of them, with 3 or more sides, can have an angle of 24 degrees.
24 sides
There is no such polygon but if you meant an interior angle of 165 then it will have 360/15 = 24 sides
If each interior angle is 165 degree then it's a regular polygon with 24 sides
Each interior angle is 165 degrees Each exterior angle is 15 degrees
If its a regular polygon and each interior angle is 165 degrees then it has 24 sides
interior angle of an n-sided polygon = (180(n-2)/n)°interior angle of a 24-sided polygon = (180x22/24)° = 165°
The interior angle is the angle formed from two sides of a nth-sided polygon. Because the polygon is regular, all angles formed from any two sides of the polygon are equal. It can be proven, but I won't attempt to, that to find the amount of sides, you use 180-[interior angle], and divide the answer by 360. In this case, 180-156=24, 360/24= 15, thus the polygon has 15 sides. One way to prove it is to imagine the polygon and divide it into isosceles triangles. But I won't go there.
Each exterior angle: 15 degrees Each interior angle: 165 degrees
If the interior angle measures 156 degrees, this means that the exterior angle is equal to 180 - 156 = 24 degrees. Dividing this by the full 360 degrees of a circle, gives 360/24 = 15. The polygon therefore has fifteen sides. A fifteen-sided polygon is called a pentadecagon or pentakaidecagon.