Question

The sum of interior angles of a polygon is eight times the sum of its exterior angles. How many sides does the polygon have?

Answer 1

Let number of sides of the polygon is $n$.

Then sum of exterior angles of the polygon is $\frac{{360}^o}{n}$.

Then sum of exterior angles be ${180}^o-\frac{{360}^o}{n}$.

Then according to the problem,

${180}^o-\frac{{360}^o}{n}=8\times \frac{{360}^o}{n}$

or, ${180}^o=9\times \frac{{360}^o}{n}$

or, $n=18$.

So number of sides is $18$.