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Question

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

A
84
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B
93
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C
105
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D
120
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Solution

The correct option is D 120
If polygon has n sides, then number of
diagonals is
nC2n=35
n(n1)2n=35
Solving we get n=10.
Thus, there are 10 vertices (as number of sides and vertices in a polygon are always equal)
The number of traingles that can be formed = 10C3=120.

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