Question

How many side would a regular polygon hav if each interior angle measure 170

Answer 1

ANSWER

$36$

EXPLANATION

Recall, that the sum of interior angles of a regular polygon is calculated using the formula;

$(n-2)180$

Hence, The measure of an interior angle (a) of a regular polygon of n sides is given by:

$a=\frac{(n-2)\times180}{n}$

Now, set this equal to 170 and solve;

$170=\frac{(n-2)\times180}{n}$

Multiply both sides by n;

$\begin{gathered} 170n=(n-2)\times180 \\ 170n=180n-360 \end{gathered}$

collect like terms;

$\begin{gathered} 170n=180n-360 \\ 360=180n-170n \\ 360=10n \\ 10n=360 \\ n=\frac{360}{10} \\ =36 \end{gathered}$

Therefore, the polygon has 36 sides.