SOLUTION: how do you find a value of a variable? there's a pentagon with numbers of degrees on only 4 sides. the fifth is a variable. how do you solve this problem?

Question 335072: how do you find a value of a variable? there's a pentagon with numbers of degrees on only 4 sides. the fifth is a variable. how do you solve this problem?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A pentagon has 5 sides.

It also has 5 angles.

The sum of the interior angles of any polygon is given by the equation:

s(a) = (n-2) * 180

a means interior angles of the polygon.
n means number of sides of the polygon.
s (a) means sum of the interior angles of the polygon.

for a triangle, that would become:

s(a) = (3-2) * 180 = 1 * 180 = 180 degrees.

for a rectangle, that would become:

s(a) = (4-2) * 180 = 2 * 180 = 360 degrees.

for a pentagon, that would become:

s(a) = (5-2) * 180 = 3 * 180 = 540 degrees.

Since you know 4 of the angles, it's a simple matter to find the measure of the 5th angle.

You simply subtract the sum of the 4 angles from 540 to get the 5th angle.

If you look at a pentagon from a geometric perspective, you can see that it forms 5 separate triangles from the center of the pentagon to the sides of the pentagon.

Just draw a dot in the center of the pentagon and then draw lines from the center of pentagon to each corner of the pentagon to see that there are 5 triangles formed.

Since the sum of the angles of a triangle is 180 degrees, this makes a total of 5 * 180 = 900 degrees.

Since the sum of the central angles of the pentagon = 360 degrees, you subtract this from 900 to get 900 - 360 = 540 degrees.

That becomes the sum of the internal angles of the polygon, which are the angles formed by the corners of the pentagon.

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