If we extend one of the sides of a polygon at a specific vertex, we create an exterior angle:

If a polygon is regular, then the following two things are true:

• All of the exterior angles are equal; and
• The size of each exterior angle is 360/n (where n is the number of sides of the polygon).

Example

As you see in the example above, we can use the exterior angle to then find the size of the interior angle. We could also then add up all of the interior angles to find the total of the interior angles in the polygon.

Exercise

Let’s use this additional knowledge in a short exercise (exercise 9 from the core textbook):

Below are the answers:

(1.) (a) a = 80º, b = 70º, c = 65º, d = 86º, e = 59º

(2.) (a) a = 36º (b) 144º

(3.) (a) (i) 40º, (ii) 20º, (iii) 8º, (iv) 6º, (b) (i) 140º, (ii) 160º, (iii) 172º, (iv) 174º

(4.) p = 101º, q = 79º, x = 70º, m = 70º, n = 130º

(5.) 24, (6.) 9, (7.) 20, (8.) 20