Final answer:
The number of triangles that can be formed by drawing diagonals from one vertex inside a 60-sided polygon is 57, as you exclude the vertex itself and its two adjacent vertices from the count.
Step-by-step explanation:
To determine the number of triangles that can be formed inside a 60-sided polygon (hexacontagon) by drawing diagonals from one vertex, we must consider that a triangle is formed by connecting any two non-adjacent vertices to our initial vertex. Since we cannot form a triangle by connecting the vertex to itself or to its two adjacent vertices, we must exclude those three vertices. Therefore, we subtract 3 from the total number of vertices.
So, the number of triangles that can be formed is:
60 (total vertices) - 1 (the vertex we are drawing from) - 2 (the two adjacent vertices) = 57 triangles.