Question

If a regular polygon has exteriorangles that measure approximately17.14° each, how many sides doesthe polygon have?

Answer 1

To answer this question we will set and solve an equation.

Recall that the exterior angle of an n-gon has a measure of:

`(360^(\circ))/(n).`

Let n be the number of sides that the polygon that we are looking for has. Since the regular polygon exterior angles with a measure of approximately 17.14 degrees, then:

`(360^(\circ))/(n)\approx17.14^(\circ).`

Therefore:

`n\approx(360^(\circ))/(17.14^(\circ))`

Simplifying the above result we get:

`n\approx21.`

Answer: 21 sides.