Chapter 11.3, Problem 4GP

To determine

To determine the number of sides the polygon has.

Answer to Problem 4GP

  $12$ sides

Explanation of Solution

Given:

Sum of the measures of the interior angle of a certain regular polygon is $1800°$ .

Formula used:

The sum of the measure of the interior angles $= \left(n-2\right)\times 180$

Calculation:

According to the question, sum of the measures of the interior angle of a certain regular polygon $=1800°$

  $\Rightarrow$ The sum of the measure of the interior angles $= \left(n-2\right)\times 180$

Here, $n$ represents number of sides.

  $\Rightarrow$ $1800°= \left(n-2\right)\times 180$

  $\Rightarrow$ $\frac{1800°}{180}= \left(n-2\right)$

  $\Rightarrow$ $10= \left(n-2\right)$

  $\Rightarrow 10+2= n$

  $\Rightarrow n= 12$

So, the number of sides $\left(n\right)=12$

Conclusion:

Therefore, the number of sides the polygon has is 12.