Question

Sandra is creating a garden in the shape of a regular polygon. If the garden has a certain number of sides, n, and has exterior angles, each with a measure of 24 degree. determine how many sides the garden has. (G.10)(1 point)

Answer 1

The number of sides the garden has is:

`15\text{ sides}`

Step-by-step explanation:

Given that each exterior angle of a regular polygon of sides n is equal to

`24^(\circ)`

Recall that the sum of exterior angles of a polygon is equal to 360 degrees.

For a n sided regular polygon with each exterior angle equal to 24 degrees, we have;

`24^(\circ)* n=360^(\circ)`

let us solve for n by dividing both sides by 24 degrees;

`\begin{gathered} (24^(\circ)* n)/(24^(\circ))=(360^(\circ))/(24^(\circ)) \\ n=15 \end{gathered}`

Therefore, the number of sides the garden has is:

`15\text{ sides}`