Question

Four angles of a polygon are ${120}^o$ each and the remaining angles are all equal to ${160}^o$ each. Find the number of sides

Answer 1

Let the number of sides are $n$

Then number of interior angles $=n$

Sum of the angles in a polygon $=(n-2){180}^{\circ }$

Four angles are ${120}^{\circ }$ and the remaining angles are all equal to ${160}^{\circ }$ each.

Then sum of the angles $=4\times 120+(n-4)160$

$=480+160n-640$

$=-160+160n$ degree

Now,

$-160+160n=(n-2)180$

$-160+160n=180n-360$

$-160+360=180n-160n$

$20n=200$

$n=10$