Q.

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

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a

exactly three sides is in common, is zero.

b

at least one side is in common, is 70.

c

exactly one side is in common, is 60

d

exactly two sides is in common, is ‘10’

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(n4)=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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