Depending on the number of sides that a polygon has, it will have a different sum of interior angles. The sum of interior angles of any polygon can be calculate by using the following formula:In this formula s is the sum of interior angles and n the number of sides of the polygon. We can check if this formula works by trying it on a triangle. A triangle has 3 sides. Since the formula says n-2, we have to take away 2 from 3 and we end up with 1. No we have to multiply it by 180° and we get 180°. This is correct since we know that the interior angles of a triangle add up to 180°. Here is a list of the most common polygons and their sum of interior angles.
Before we start looking at how to calculate the exterior angles, you first need to know what they are. On the right you can see a hexagon with two exterior angles marked in red. We have extended two lines of the hexagon. The angle between this line and the original shape is the exterior angle.It is very easy to calculate the exterior angle it is 180 minus the interior angle. The formula for this is:We can also use 360 divided by n (number of sides of the regular polygon) to find the individual exterior angles. This works because all exterior angles always add up to 360°.Look at the example underneath!
ExampleIn this example, we have an octagon of which we want to find the interior and exterior angle. We will use the formulas from above to do so!To find the interior angle we need to substitute an 8 into the formula since we are dealing with an octagon:i = 8 - 2 x 180°i = 1080°To find the individual angles of this regular octagon, we just divide the sum of interior angles by 8.As a result, every angle is 135°.To find the exterior angle we simply need to take 135 away from 180. This is equal to 45. Consequently, eachexterior angle is equal to 45°. To find the sum of exterior angles, we simply multiply this by 8. This is equal to 360°.
The next step of your study of angles is to learn some angle properties. These will become really helpful when solving angle problems as you will easily be able to find missing angles. Please share this page if you like it or found it helpful!
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Chapter 27.1:Learning OutcomesStudents will learn about the relationship between the interior angles of different shapes!Students will learn about the relationship between the exterior angles of different shapes!