For which numbers n can it happen that a not necessarily con

For which numbers n can it happen that a (not necessarily convex) pentagon has exactly n diagonals lying entirely in its interior? For each possible n, draw an example of a pentagon with exactly that many such \"internal diagonals\".

Solution

Sides in pentagon is S=5

No of diagonals in any polygon is given by S(S-3)/2

Where S is the total number of sides in a polygon.

Since in pentagon S=5

Therefore total diagonals in pentagon is given by

5(5-3)/2 = 5

Hence for n =5 pentagon has exactly n diagonals.