Solve problems involving exterior angles

﻿In this lesson, we're going to be finding missing exterior angles of polygons. What is a polygon? A polygon is a 2D shape but it's made up of entirely of straight lines. These are some examples of different kinds of polygons. This is a polygon. I've extended each of the lines of this polygon. These angles I've highlighted are the exterior angles. These are the interior angles. What do you notice about the interior and exterior angles? Well done If you thought that they would add up to 180 degrees. As they are at the same point on a straight line, the interior and exterior angles of polygons sum to 180 degrees. Let's try and find this missing angle on the straight line. Angles on a straight line sum to 180. To work out this missing angle, we need to calculate 180 subtract 127, which is 53. So this missing angle is 53 degrees. What about angles around a point? Angles around a point sum to 360. To find this missing angle, we need to add together the three angles that we've already got. This makes 245 degrees. To work out the missing angle, we're going to do 360 subtract 245. This gives an answer of 115. So this missing angle is 115 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. To find all of these missing angles, you needed to use the fact that angles that meet at a point on a straight line sum to 180 degrees. The sum of all of the exterior angles in both part A and B is 360. Exterior angles of a polygon sum to 360. We need to find the size of the exterior angle labelled A. We know that the four exterior angles need to add up to make 360. Let's start by adding up the three angles that we already have. This gives us 320 degrees in total. To work out the size of angle A, going to do 360 subtract 320, which is 40. So angle A is 40 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. The sum at the exterior angles of any polygon is 360 degrees. You can then use this fact to find the missing exterior angles of each of these polygons. What is a regular polygon? We know that a polygon is a 2D shape made up of straight lines only. A regular polygon is a polygon that has all sides the same length and where all of the angles are equal. These are some examples of regular polygons. We know that the exterior angles of any polygon sum to 360 degrees. If we look at this regular polygon, which is an equilateral triangle, we can see that all three of the exterior angles are going to be equal. To work out the size of each of these angles, we're going to divide 360 by three, as there are three equal angles. This gives us 120 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. To find the exterior angles of any regular polygon, you need to divide 360 by the number of 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. The expression that can be written to represent the exterior angle of a regular polygon with N sides is 360 divided by N. In question six, if a regular polygon has an exterior angle of 45 degrees, we can divide 360 by X to give us the number of sides. This question, the answer is eight. That's all for this lesson. Thanks for watching.

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?

Find Missing Exterior Angles of Polygons

In this lesson, we will calculate missing exterior angles of any regular or irregular polygon.

Maths

Y11 Maths (Foundation)

Key Stage 4

Year 11

Miss

Find missing exterior angles of polygons

Polygons 2 (Interior and Exterior)

Shape and Space (S)

THEME

UNIT

Finding the sum of interior angles in a polygon

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

Find missing angles when two or more polygons are joined

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?

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?

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 missing exterior angles of polygons

Core Content

Polygons 2 (Interior and Exterior):