Chapter 11, Problem 27SGR

To determine

To find the measure of an interior angle.

Answer to Problem 27SGR

  $2880°$

Explanation of Solution

Given Information: 18-gon.

Formula Used: A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles = $(n-2)\times 180°$ . To find the measure of one interior angle, take that formula and divide by the number of sides $n$ = $\frac{(n-2)\times 180°}{n}$

Calculation:

Sum of interior angles: $(n-2)\times 180°$

18-gon has 18 sides. Hence,

Sum of interior angles of 18-gon: $(18-2)\times 180°$

So,

Sum of interior angles of 18-gon: $16\times 180°$

Sum of interior angles of 18-gon: $2880°$

Each angle of 18-gon: $\frac{(n-2)\times 180°}{n}$

Each angle of 18-gon: $\frac{(18-2)\times 180°}{18}$

Each angle of 18-gon: $\frac{2880°}{18}$

Each angle of 18-gon: $160°$