Final answer:
From a 13-gon, 66 triangles can be formed using diagonals from a common vertex by choosing 2 out of the remaining 12 vertices to form a triangle with the common vertex, calculated using the combinations formula.
Step-by-step explanation:
When you want to find out how many triangles can be formed using diagonals from a common vertex in a 13-gon (a polygon with 13 sides), you can think of it in terms of combination of points. You need 2 more points to form a triangle with the common vertex. As there are 12 other vertices in the 13-gon, you will be choosing 2 out of these 12 vertices to form a triangle. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items, r is the number of items to choose, and ! denotes factorial.
Using this formula, the number of triangles that can be formed from a 13-gon using diagonals from a common vertex is 12C2, which is 12! / (2!(12-2)!) = 66. Therefore, you can form 66 triangles.