1. **Problem Statement:** We need to find how many triangles can be formed by drawing diagonals from a common vertex in a regular octagon (8-sided polygon). 2. **Formula and Explanation:** When you draw diagonals from one vertex of an $n$-sided polygon, the polygon is divided into $n-2$ triangles. 3. **Apply the formula:** For an octagon, $n=8$. 4. **Calculate:** $$ \text{Number of triangles} = n - 2 = 8 - 2 = 6 $$ 5. **Interpretation:** This means from any one vertex of an octagon, you can form 6 triangles by drawing diagonals to the other vertices. 6. **Final answer:** The number of triangles formed is **6**.