Chapter 7, Problem 15RP

To determine

The number of diagonals that can be drawn in a pentadecagon are to be calculated

Answer to Problem 15RP

The number of diagonals is $d=90$

Explanation of Solution

Given information : A pentadecagon is fifteen-sided polygon.

Formula used:The number of the diagonal is given by the following formula

  $d=\frac{n(n-3)}{2}$

Where

“ n ” is the number of the sidesCalculation : We know that for a n sided polygon, the number of diagonals that can be drawn on it are calculated as

  $d=\frac{n(n-3)}{2}$

Now, we put the value of n as fifteen in the given formula, thus we get

  $d=90$