Let `T_n` be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If `T_(n+1)-T_n=""10` , then the value of n is (1) 5 (2) 10 (3) 8 (4) 7

Explanation

To solve the problem, we need to find the value of \( n \) such that the difference between the number of triangles formed by an \( n+1 \)-sided polygon and an \( n \)-sided polygon is equal to 10.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find the number of triangles that can be formed by the vertices of an \( n \)-sided polygon. The number of triangles \( T_n \) formed by choosing 3 vertices from \( n \) vertices is given by the combination formula \( \binom{n}{3} \).

2. **Formula for \( T_n \)**:
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