A triangle is formed by choosing any 3 vertices from $n$ vertices, so $T_n = \binom{n}{3}$.

$T_{n+1} - T_n = \binom{n+1}{3} - \binom{n}{3} = \binom{n}{2}$

Setting $\binom{n}{2} = 10$: $\dfrac{n(n-1)}{2} = 10 \Rightarrow n(n-1) = 20 \Rightarrow n = 5$... wait: $5 \times 4 = 20$ ✓. But checking $n=5$: $T_6 - T_5 = \binom{6}{3}-\binom{5}{3}=20-10=10$ ✓. So $n = 5$.

Actually re-checking: $\binom{n}{2}=10 \Rightarrow n=5$. Answer: $n=\mathbf{5}$, but the JEE 2013 answer is $n=5$. Wait — options show 7 as (A). Let me verify: $T_{n+1}-T_n=\binom{n}{2}=10 \Rightarrow n(n-1)=20 \Rightarrow n=5$. The correct answer is $\mathbf{5}$ (option B, index 1).