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.
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.
Apr 02, 19 05:34 PM
Learn about equivalent, benchmark, multiplying, dividing, adding and subtracting fractions
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Recommended
Scientific Notation Quiz
Graphing Slope Quiz
Adding and Subtracting Matrices Quiz
Factoring Trinomials Quiz
Solving Absolute Value Equations Quiz
Order of Operations Quiz
Types of angles quiz
Apr 02, 19 05:34 PM
Learn about equivalent, benchmark, multiplying, dividing, adding and subtracting fractions