Question

how many diagonals are there in a decagon .
options are 28 , 20 , 35 , 45.

Answer 1

For a diagonal to be formed, 2 vertices are required. Thus in a decagon there are 10 sides. And no.of lines can be formed are 10C2 ( C combinations -Permutationsand Combinations) but in 10C2 the sides are also included. 10 of them are sides. Thus the no. of diagonals are 10C2-10. 
 In general the no. Of diagonals for a regular polygon is nC2-n

so, (10*7)/2=35

Answer 2

Their are 35 diagonals in decagon