Answered

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

If A Regular Polygon Has Exteriorangles That Measure Approximately1714 Each How Many Sides Doesthe Polygon Have class=

Sagot :

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

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

[tex]\frac{360^{\circ}}{n}.[/tex]

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:

[tex]\frac{360^{\circ}}{n}\approx17.14^{\circ}.[/tex]

Therefore:

[tex]n\approx\frac{360^{\circ}}{17.14^{\circ}}[/tex]

Simplifying the above result we get:

[tex]n\approx21.[/tex]

Answer: 21 sides.

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