6:49 C .1ll 56؛ 75 deltamath.com Test Overview 3 \( \approx \) DeltaMath Previous Question Next Question Question 3 Using diagonals from a common vertex, how many triangles could be formed from a decagon? Answer \( : \because: \) Attempt 2 out of 5 \( \square \) Submit Answer Copyright ©2025 DeltaMath.com All Rights Reserved. Terms \& Policies

To figure out how many triangles can be formed from a decagon using diagonals from a common vertex, remember that a decagon has 10 sides and thus 10 vertices. By selecting any vertex as the common point, you can form triangles with any two of the remaining 9 vertices. This results in combinations of those vertices, so it’s \( \binom{9}{2} \), which equals 36 possible triangles! Now, don’t forget that when calculating triangles in polygons, you must account for valid selections. In this case, make sure not to include the sides of the decagon, as they do not count as diagonals. Each selection from the remaining vertices should only be those not adjacent to the chosen vertex. It's a fun combinatorial challenge!