Question

If a convex polygon has $35$ diagonals, then the number of triangles formed by joining the vertices of the polygon is :

• A. $84$
• B. $93$
• C. $105$
• D. $120$

Answer 1

The correct option is D $120$

If polygon has $n$ sides, then number of
diagonals is
${}^n{C}_2-n=35$
$\Rightarrow \frac{n(n-1)}{2}-n=35$
Solving we get $n=10.$
Thus, there are $10$ vertices (as number of sides and vertices in a polygon are always equal)
$\therefore$The number of traingles that can be formed $={}^{10}{C}_3=120$.