(n x n - 3n)/2
(24 x 24 - 3x24)/2
(576 - 72)/2
504/2
= 252
To determine the number of sides ( n ) in a polygon with 252 diagonals, we use the formula for the number of diagonals in a polygon: ( D = \frac{n(n-3)}{2} ). Setting this equal to 252 gives us the equation ( \frac{n(n-3)}{2} = 252 ). Solving this leads to ( n(n-3) = 504 ), or ( n^2 - 3n - 504 = 0 ). The positive solution to this quadratic equation is ( n = 24 ), so the polygon has 24 sides.
0.5*(82-24) = 20 diagonals
An n-sided polygon or n-gon, just like it sounds, has n sides. For example, a 13-sided polygon has 13 sides. A 24-gon has 24 sides.
Basically when you have a 24 sided polygon you can split it up into 22 separate, non-overlapping triangles by drawing diagonals. Each triangle has 180 degrees, so the product, 22 times 180, gives you the sum of the interior angles of the 24 sided polygon.
If the polygon is regular, the measure of one interior angle of a 24 side polygon is 165 degrees.
24 diagonals
252 diagonals
To determine the number of sides ( n ) in a polygon with 252 diagonals, we use the formula for the number of diagonals in a polygon: ( D = \frac{n(n-3)}{2} ). Setting this equal to 252 gives us the equation ( \frac{n(n-3)}{2} = 252 ). Solving this leads to ( n(n-3) = 504 ), or ( n^2 - 3n - 504 = 0 ). The positive solution to this quadratic equation is ( n = 24 ), so the polygon has 24 sides.
0.5*(82-24) = 20 diagonals
An n-sided polygon or n-gon, just like it sounds, has n sides. For example, a 13-sided polygon has 13 sides. A 24-gon has 24 sides.
An eight-sided polygon has 8 vertices. Consider1st vertex = 7 diagonals to other vertices2nd vertex = 6 diagonals to other vertices (since one has now been used)3rd vertex = 54th vertex = 45th vertex = 36th vertex = 27th vertex = 18th vertex = 0, so7+6+5+4+3+2+1 = 28Improved Answer:-Formula for finding diagonals of a polygon 0.5*(n2-3n) when n is the number of sides0.5*(82-24) = 20 diagonals
Basically when you have a 24 sided polygon you can split it up into 22 separate, non-overlapping triangles by drawing diagonals. Each triangle has 180 degrees, so the product, 22 times 180, gives you the sum of the interior angles of the 24 sided polygon.
15
If the polygon is regular, the measure of one interior angle of a 24 side polygon is 165 degrees.
24
There are 22
Providing that it's a regular polygon then: 360/15 = 24 sides