Sum of all exterior angles of a polygon

To help you see what the sum of all exterior angles of a polygon is, we will use a square and then a pentagon. Since it is very easy to see what the sum is for a square, we will start with the square.

Exterior angles

Notice that an exterior angle is formed by a side of the square and an extension of an adjacent side. For example, x, y, z, and w are exterior angles.

Each interior angle in a square is equal to 90 degrees. Notice that an interior angle plus the adjacent exterior angle is equal to 180 degrees.

Interior angle  +  adjacent exterior angle = 180 degrees.

For example, 90 + w = 180 degrees

w = 90 degrees

Since there are 4 exterior angles, 4 x 90 = 360 degrees.

To find the measure of the interior angle of a pentagon, we just need to use this formula.

[(n - 2 ) 180] / n 

Since n is equal to 5, [(n - 2 ) 180] / n = [(5 - 2) 180] / 5 = [3 x 180] / 5 = 540 / 5 = 108

Again, Interior angle  +  adjacent exterior angle = 180 degrees.

108 + adjacent exterior angle = 180 degrees

adjacent exterior angle = 180 - 108 = 72

Since there are 5 exterior angles, 5 x 72 = 360 degrees.

It does not matter how many sides the polygon has, the sum of all exterior angles of a polygon is always equal to 360 degrees. 

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