Chapter 7.3, Problem 24PSD

To determine

To calculate : The set of the polygons

Answer to Problem 24PSD

The set of the polygons is with $n>361$ sides

Explanation of Solution

Given information : The following information is given

Number of diagonals is greater than the sum of the measures of the angles

Formula used : The number of diagonals is found by

  $d=\frac{n(n-3)}{2}$

The sum of the measures of the angles is given by

  $s=(n-2){180}^0$

Calculation : We use the above two formulas and equate them. Thus, we get

  $\frac{n(n-3)}{2}>(n-2)180$

Hence, on simplifying the equation, we get

  $n>361$