Chapter 8.1, Problem 7PSA

To determine

To find:The ratio of number of diagonals in a pentagon and to the measure of each exterior regular decagon.

Answer to Problem 7PSA

The ratio is $\frac{5}{36}$

Explanation of Solution

Given information The number of diagonals of a pentagon (side ( n )= 5)

The exterior angle of the regular decagon $={36}^o$

Formula used

The number of diagonals in a regular polygon of sides ‘ n’ can be calculated using

  $\frac{n\left(n-3\right)}{2}$

Calculation The number of diagonals in a pentagon will be given by

  $\frac{n\left(n-3\right)}{2}$

On substituting the, $n=5$

  $\begin{array}{l}=\frac{5\left(5-3\right)}{2}\\ =\frac{5\times 2}{2}\\ =5\end{array}$

  $\therefore$ Ratio of diagonals in a pentagon and exterior angle of regular decagon

  $=\frac{5}{36}$