How many diagonals can be drawn from each vertex of a decagon?

A diagonal of a polygon is a line segment that is obtained by joining any two non-adjacent vertices.

Answer: The number of diagonals that can be drawn from each vertex of a decagon is 7.

Let's look into the solution.

Explanation:

A decagon is a ten-sided polygon with ten vertices and ten angles.

Let's assume a decagon with all of its vertices going outward (as all of its angles are less than 180°).

Since there are 10 vertices, hence, a line can be drawn from each vertex towards the remaining 9 vertices. But 2 of these lines will not be diagonals as they are themselves the sides of the decagon.

So each of the 10 vertices will have 9 – 2 = 7 diagonals each.

Thus, the number of diagonals that can be drawn from each vertex of a decagon is 7.