Question

is the number of diagonals and number of sides in a polygon differ by 18 then the sum of the angles in a polygon is

Answer 1

The number of sides should be same as number of vertex. Let's say the number of vertex is n. How many diagonals are possible now?

Let's select a random vertex. This can be done in n ways. How many diagonals are possible through this particular vertex. We need to join all other vertices except two consecutive vertex to this particular vertex. So it would be n-3.

Hence total number of diagonals are n(n-3)/2. We need to divide here by two as every diagonal is getting counted twice.

So, n(n-3)/2= 170, solving which gives n = 20 (Answer)