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The number of triangles formed by the vertices of decagon such that each triangle and decagon have.

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exactly one side is in common, is 60

exactly two sides is in common, is ‘10’

exactly three sides is in common, is zero.

at least one side is in common, is 70.

answer is A, B, C, D.

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Detailed Solution

n= No. of vertices of decagon = 10. No. of $Δ$ less
(i) with exactly one side common = $n (n - 4) = 60$
(ii) with exactly two sides common = n=10
(iii) with exactly there sides common = 0
(iv) at least one side common = 60+10=70.

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