You can form 7 triangles using diagonals from a common vertex in the hexagon pictured.
Based on the image you sent, which shows a hexagon, here's how many triangles you can form using diagonals from a common vertex:
Formula for triangles from a common vertex: The formula for the number of triangles formed from a polygon using diagonals from a common vertex is n - 2, where n is the number of sides in the polygon.
Applying the formula: In this case, the polygon has 9 sides (n = 9). Therefore, using the formula, we get 7 triangles (n - 2 = 9 - 2 = 7).
Justification for one common vertex: Since the question specifies "using diagonals from a common vertex," it implies selecting only one vertex as the starting point for drawing diagonals.
This is usually the case with odd-sided polygons, where using multiple common vertices wouldn't result in significantly more triangles.
Therefore, you can form 5 triangles using diagonals from a common vertex in the hexagon pictured.