Question

If each interior angle of a polygon is 14 times its exterior angle , the number of sides of the polygon is

Answer 1

Step-by-step explanation:

here's your answer...

the measure of each interior angle of a regular polygon is 14 times the measure of an exterior angle. how many sides does the polygon have?

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The interior and its corresponding exterior angle are supplementary.

x + 14x = 180

15x = 180

x = 12 degrees (the exterior angle)

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Fact: The sum of the exterior angles is 360 degrees

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# of exterior angles = 360/12 = 30

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# of sides = # of exterior angles = 30

hope it helps you:)

Answer 2

Answer:

If each interior angle of a polygon is 14 times its exterior angle, the number of sides of the polygon is 30

Explanation:

Given:
The Interior angle of a polygon is 14 times its exterior angle

To Find:

The number of sides of the polygon

Solution:
The outer angle plus the next interior angle equal to 180 degrees

Thus, External Angle + Internal angle = 180

e + i = 180

Because each interior angle is 14 times as large as its neighboring exterior angle, i = 14e

e + 14e = 180

15e = 180

e = 12 degrees

We know that the measure of an exterior angle is e = 360/n degrees where n is the number of sides

As, e = 12

n = $\frac{360}{12}= 30$

Hence, the number of sides is 30

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