Chapter 9, Problem 3CR

a

To determine

To find:The sum of the angles of a nonagon

Answer to Problem 3CR

The sum is $s={1260}^0$

Explanation of Solution

Given information:for a nonagon, we have number of sides as nine.

Formula used:The sum of the angles of any polygon are

  $s=(n-2){180}^0$

Where, n is the number of sides of the polygon

Calculation:We find the sum of the angles of a polygon as

  $s=(n-2){180}^0$

Where, n is the number of sides of the polygon, which is nine in this case. Hence, we can say that for nonagon,

  $s=(9-2){180}^0=7({180}^0)={1260}^0$

b

To determine

To find:The number of sides of the polygon

Answer to Problem 3CR

The number of sides is $n=30$

Explanation of Solution

Given information:The value of each angle is given as

  $x={168}^0$

Formula used:The sum of the angles of any polygon are

  $s=(n-2){180}^0$

Where, n is the number of sides of the polygon

Calculation:We find the of the angles of a polygon as

  $x=\frac{(n-2){180}^0}{n}={168}^0\to n=30$

c

To determine

To find:The number of diagonals in a heptagon

Answer to Problem 3CR

The number of diagonals are $d=9$

Explanation of Solution

Given information:for a heptagon, we have number of sides as six.

Formula used:The sum of the angles of any polygon are

  $s=(n-2){180}^0$

Where, n is the number of sides of the polygon

Calculation:We find the number of the diagonals of a polygon as

  $d=\frac{n(n-3)}{2}$

Where, n is the number of sides of the polygon. Hence, we can say that for nonagon,

  $d=\frac{6(6-3)}{2}=9$