Question

The difference between any two consecutive interior angles of a polygon is $5^o$. If the smallest angle is ${120}^o$, find the number of sides of the polygon.

Answer 1

Let the nth interior angle are ${120}^{\circ }+5(n-1{)}^{\circ }$

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

${\Sigma }_n{115}^{\circ }+5{\Sigma }_n{n}^{\circ }=180n^{\circ }-{360}^{\circ }⟹n=9,16$