Question

Four angles of a polygon are $100°$ each. The remaining angles are $160°$ each. Find the number of sides of the polygon.

Answer 1

Calculate the number of sides of the polygon

Let $n$ be the number of sides. Then,

Sum of all interior angles of a polygon $=(n-2)\times 180$

Given, four angles measure $100°$ each and the remaining angles measure $160°$ each. Thus,

$$\begin{gathered} 4\times 100+(n-4)\times 160=(n-2)\times 180 \\ \Rightarrow 400+160n-640=180n-360 \\ \Rightarrow 760-640=20n \\ \Rightarrow n=6 \end{gathered}$$

Therefore, the number of sides of the polygon is $6$.