A decagon is a polygon with ten sides. To determine how many diagonals can be drawn from each vertex of a decagon, we can use a simple formula for calculating diagonals in any polygon.
The formula for the number of diagonals (D) in a polygon with n sides is given by:
D = n(n – 3) / 2
In the case of a decagon, where n = 10, we substitute the value into the formula:
D = 10(10 – 3) / 2 = 10(7) / 2 = 70 / 2 = 35
This means that a decagon has a total of 35 diagonals. However, since the question asks specifically about the diagonals that can be drawn from each individual vertex, we need to tweak our approach.
From any given vertex in a decagon, you can connect to 10 – 1 = 9 other vertices (since you can’t connect to itself). However, 2 of these connections are the edges of the decagon, meaning you cannot draw diagonals from those connections. Therefore, the number of diagonals from one vertex is:
9 – 2 = 7
So, from each vertex of a decagon, you can draw 7 diagonals. Thus, the answer to the question is:
7 diagonals can be drawn from each vertex of a decagon.