Solution:

An octagon is a polygon with eight sides and eight vertices.

To find the number of diagonals that can be drawn by joining the vertices of an octagon, we can use the formula:

Number of diagonals = n(n-3)/2

where n is the number of sides of the polygon.

Substituting n = 8 in the formula, we get:

Number of diagonals = 8(8-3)/2 = 20

Therefore, the correct option is (a) 20.

Explanation:

When we join any two non-adjacent vertices of a polygon, we get a diagonal. In an octagon, there are 8 vertices. Let's consider one vertex and count the number of diagonals that can be drawn from it.

From one vertex, we can draw diagonals to 5 other vertices (excluding the adjacent vertices). Therefore, we have 5 options for the first endpoint of the diagonal.

For the second endpoint of the diagonal, we can choose any of the remaining 6 vertices (excluding the two adjacent vertices and the vertex we started from). Therefore, we have 6 options for the second endpoint of the diagonal.

However, we have counted each diagonal twice (once from each endpoint). Therefore, we need to divide the total count by 2 to get the actual number of diagonals.

Using this method, we can count the number of diagonals for each of the 8 vertices and add them up to get the total number of diagonals.

Alternatively, we can use the formula mentioned above to directly calculate the number of diagonals.