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The sum of the interior angles of a polygon with 10 sides be expressed as 360n. What is the value of n?

The Sum Of The Interior Angles Of A Polygon With 10 Sides Be Expressed As 360n What Is The Value Of N class=

Sagot :

The sum S of the interior angles of a polygon is

S = (m - 2) * 180º

where m is the number of sides of the polygon.

Then, since the given polygon has 10 sides, m = 10, and its sum is:

S = (10 - 2) * 180º = 8 * 180º = 1440º

Now, since this sum is expressed as 360n, we have:

360n = 1440

n = 1440/360

n = 4

Therefore, the second option is correct.

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