Question

Alexander is building an enclosure in the shape of a regular polygon. If the enclosure has a certain number of sides, n, and has exterior angles, each with a measure of 32.7 degrees, determine how many sides the garden has. 9 sides 10 sides 11 sides 12 sides

Answer 1

To calculate the measure of the external angles of a regular polygon, you have to divide 360º by the number of sides:

$\angle\theta=\frac{360º}{n}$

If the external angles have measure ∠θ=32.7º

Replace this measure in the expression and calculate for n

$\begin{gathered} 32.7=\frac{360}{n} \\ 32.7n=360 \\ n=\frac{360}{32.7} \\ n=11.009 \end{gathered}$

The regular polygon has 11 sides and is called hendecagon