What is the sum of interior angles of a 20-sided shape?

What is the sum of interior angles of a 9-sided shape?

What is the missing angle, labelled x?

What is the size of each interior angle in a regular octagon?

Finding the Sum of Interior Angles

﻿In this lesson we're going to be calculating the number of sides that a polygon has when we're given the sum of interior angles. A polygon has interior angles that sum to 540 degrees. We've been asked to work out the number of sides that the polygon has. The sum of interior angles can be found by calculating n subtract two multiplied by 180, where n is the number of sides. If we substitute 540 into this formula we have this equation. To begin solving it we're going to divide both sides by 180. This gives us three is equal to n subtract two. The inverse of subtracting two is adding two. So let's add two to both sides. This gives n equals five. N is the number of sides, so this polygon has five sides. Here are some questions for you to try. Pause the video to complete your task and resume once you're finished. Here are the answers. To find the number of sides you need to divide the sum of interior angles by 180 and then add two. The regular polygon had interior angles that summed to 540 degrees. A regular polygon has all angles that are equal. The first thing we need to do in order to find the size of each interior angle is to calculate the number of sides that this regular polygon has. The sum of interior angles is worked out by calculating n subtract two multiplied by 180, where n is the number of sides. So 540 is equal is to n subtract two multiplied by 180. Using inverse operations we're going to solve this equation to find n, which is the number of sides. First, let's divide both sides by 180. This means that three is equal to n subtract two. Next, we're going to add two to both sides. So our regular polygon has five sides. To find the size of each interior angle we're going to divide 540 by five. This gives us 108 degrees. Here are some questions for you to try. Pause the video to complete your task and resume once you're finished. Here are the answers. Once you have found the number of sides that each polygon has divide the sum of interior angles by this. The regular polygon had interior angles that summed to 540 degrees. We've been asked to work out the size of each exterior angle. So the first thing we need to do is to work out the number of sides that this regular polygon has. Interior angles of a polygon are calculated by doing n subtract two multiplied by 180, where n is the number of sides. We know that the interior angles in our regular polygon sum to 540. So 540 is equal to n subtract two multiplied by 180. Using inverse functions we're going to solve this equation to find that the regular polygon has five sides. Exterior angles are calculated by dividing 360 by the number of sides, as in a regular polygon all exterior angles are equal and sum to 360. We're going to do 360 divided by five, which gives us the exterior angle of 72 degrees. Here are some questions for you to try. Pause the video to complete your task and resume once you're finished. Here are the answers. After finding the number of sides that each polygon has divide 360 by this, because the the exterior angles of any polygon sum to 360 degrees. That's all for this lesson! Thanks for watching.

The sum of interior angles of a polygon is 720º. How many sides does the polygon have?

The sum of interior angles of a polygon is 2880º. How many sides does the polygon have?

The sum of interior angles of a regular polygon is 3960º. What is the size of each interior angle of the regular polygon?

The sum of interior angles of a regular polygon is 5040º. What is the size of each exterior angle of the regular polygon?

Find the Number of Sides when given the Sum of Interior Angles

In this lesson, we will find the number of sides of a polygon when given only the sum of interior angles.

Maths

Y11 Maths (Foundation)

Key Stage 4

Year 11

Miss

Find the number of sides when given the sum of interior angles

Polygons 2 (Interior and Exterior)

Shape and Space (S)

THEME

UNIT

Find missing exterior angles of polygons

Finding the sum of interior angles in a polygon

Find missing angles when two or more polygons are joined

What is the sum of exterior angles of any polygon?

Calculate the size of angle a.

Calculate the size of angle b.

4. What is the size of each exterior angle of a regular 15 sided polygon?

5. A regular polygon has an exterior angle of 30º. How many sides does it have?

The diagram shows two hexagons joined. Calculate the size of the angle marked b.

A regular pentagon and a regular hexagon are joined. Calculate the size of angle a.

An octagon and a nonagon are joined. Calculate the size of the angle labelled g.

Lesson overview:Find the number of sides when given the sum of interior angles

Core Content

Polygons 2 (Interior and Exterior):