Polygon Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium

Each interior angle of a regular polygon is

150°

. How many sides does it have?

Solution

1
Step 1: For a regular polygon, each interior angle $= \dfrac{(n-2) \times 180°}{n}$ .
2
Step 2: Set equal to $150°$ : $\dfrac{(n-2) \times 180}{n} = 150$ .
3
Step 3: Multiply both sides by $n$ : $(n-2) \times 180 = 150n$ .
4
Step 4: Expand and solve: $180n - 360 = 150n \Rightarrow 30n = 360 \Rightarrow n = 12$ .

Answer

12 sides (regular dodecagon)

By setting the regular polygon interior angle formula equal to the given angle and solving, we find the number of sides. Alternatively, each exterior angle