Question

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

Answer 1

`36`

Step-by-step 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=((n-2)*180)/(n)`

Now, set this equal to 170 and solve;

`170=((n-2)*180)/(n)`

Multiply both sides by n;

`\begin{gathered} 170n=(n-2)*180 \\ 170n=180n-360 \end{gathered}`

collect like terms;

`\begin{gathered} 170n=180n-360 \\ 360=180n-170n \\ 360=10n \\ 10n=360 \\ n=(360)/(10) \\ =36 \end{gathered}`

Therefore, the polygon has 36 sides.