48 because (50-2)*180 = sum of interior angles
21
In a polygon with n sides, the number of diagonals that can be drawn from one vertex is given by the formula (n-3). Therefore, in a 35-sided polygon, you can draw (35-3) = 32 diagonals from one vertex.
If all of the diagonals are drawn from a vertex of an octagon, how many triangles are formed
By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles. With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so: sum_of_interior_angles = 180 x (number_of_sides - 2)
In a 54-sided polygon, 53 possible diagonals can be drawn from one vertex to another. These diagonals will not intersect. Therefore, the interior will be divided into 54 regions by the 53 diagonals plus the two sides of the original polygon that adjoin the vertex from which the diagonals are drawn.
Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.
98
21
98
A polygon with ( n ) sides can be divided into ( n - 2 ) triangles by drawing all the diagonals from one vertex. This is because each diagonal connects the chosen vertex to another vertex, forming a triangle with each adjacent pair of vertices. Therefore, for a polygon with ( n ) sides, you will create ( n - 2 ) triangles in total.
It is: 8-2 = 6 triangles
Number of sides minus 2 equals the number of triangles within the polygon.
In a polygon with n sides, the number of diagonals that can be drawn from one vertex is given by the formula (n-3). Therefore, in a 35-sided polygon, you can draw (35-3) = 32 diagonals from one vertex.
If all of the diagonals are drawn from a vertex of an octagon, how many triangles are formed
In a polygon with ( n ) sides, the number of diagonals that can be drawn from one vertex is given by the formula ( n - 3 ). For a polygon with 35 sides, this means you can draw ( 35 - 3 = 32 ) diagonals from one vertex. Thus, from one vertex in a 35-sided polygon, you can draw 32 diagonals.
By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles. With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so: sum_of_interior_angles = 180 x (number_of_sides - 2)
A hexagon can be divided into four triangles by drawing all of the diagonals from one vertex. Since a hexagon has six sides, drawing diagonals from one vertex creates three additional triangles, resulting in a total of four triangles (the original triangle formed by the vertex and two adjacent vertices, plus the three formed by the diagonals).