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Calculate External Angles of a Polygon

In this worksheet, students will calculate the external angles of a polygon.

'Calculate External Angles of a Polygon' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions, Angles

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Boy with phone

 

Lost again? Not to worry the GPS on your phone can help you find your way.

GPS uses angles, including exterior angles to help with the directions.  The mathematics is quite complex but has to start with the basics like we are going to here.

 

exterior angles example

 

 

exterior angles example

 

 

Because the exterior angles of a triangle will fit around a point, and we know that angles around a point add up to 360°

We just use this along with the number of sides of the polygon to find the exterior angle.

 

Hopefully, now you won't get lost.

hexagon

 

Calculate the size of the exterior angle of this hexagon.

55°

40°

60°

65°

nonagon

 

55°

40°

60°

65°

decagon

 

Calculate the exterior angle of this shape.

55°

40°

60°

65°

Boy

 

Can you help me?  I need to find the exterior angle of a polygon.

How do I do this?

 Divide the number of sides by 360°Multiply the number of sides by 360°Divide 360 by the number of sides
To find the exterior angle of any polygon

child looking confused

 

What is the exterior angle of a 20 sided shape?

 Divide the number of sides by 360°Multiply the number of sides by 360°Divide 360 by the number of sides
To find the exterior angle of any polygon

 

If a shape has an exterior angle of 24° how many sides does it have?

Match up time.  Find the number of sides of a regular polygon with these exterior angles.

Column A

Column B

10°
60
24
72
15°
36

triangle

Find the value of x

Write your answer in figures without the units.

Column A

Column B

10°
60
24
72
15°
36

Shape A is a 12 sided shape with an exterior angle of 3x.

The exterior angle of shape B is 2x.

external angle algebra

 

 36°12°10°12161518
The value of x is
the number of sides shape B has is

 

What is the exterior angle of an 11 sided shape?

Round your answers to 1 decimal place (1 d.p)

 36°12°10°12161518
The value of x is
the number of sides shape B has is
  • Question 1

hexagon

 

Calculate the size of the exterior angle of this hexagon.

CORRECT ANSWER
60°
EDDIE SAYS
Did you remember the sum from the question before? A hexagon has six sides so all we do is: 360 ÷ 6 = 60°
  • Question 2

nonagon

 

CORRECT ANSWER
EDDIE SAYS
Hopefully, that sum is becoming ingrained in your brain! The exterior angle of this nonagon is 40° because 360 ÷ 9 = 40° Are you navigating these activities well?
  • Question 3

decagon

 

Calculate the exterior angle of this shape.

CORRECT ANSWER
EDDIE SAYS
Okay, so you weren't given the number of sides... but that's not a problem you just need to count them. This is a decagon, a 10 sided shape , so to calculate the exterior angle 360 ÷ 10 = 36°
  • Question 4

Boy

 

Can you help me?  I need to find the exterior angle of a polygon.

How do I do this?

CORRECT ANSWER
 Divide the number of sides by 360°Multiply the number of sides by 360°Divide 360 by the number of sides
To find the exterior angle of any polygon
EDDIE SAYS
It is quite simple really isn't it? Make sure you get the calculation the correct way around, otherwise you will get some weird and wonderful answers.
  • Question 5

child looking confused

 

What is the exterior angle of a 20 sided shape?

CORRECT ANSWER
EDDIE SAYS
Bring it on! It doesn't matter about the number of sides, does it? 360 ÷ 20 = 18°. We use 360 a lot in maths to help solve problems, a useful number don't you think?
  • Question 6

 

If a shape has an exterior angle of 24° how many sides does it have?

CORRECT ANSWER
15
EDDIE SAYS
You know how to find the exterior angle by taking 360 and dividing by the number of sides. So to find the number of sides take 360 and divide by the angle given and. hey presto! 360 ÷ 24 = 15 sides
  • Question 7

Match up time.  Find the number of sides of a regular polygon with these exterior angles.

CORRECT ANSWER

Column A

Column B

10°
36
60
72
15°
24
EDDIE SAYS
External angles or number of sides no bother. What a great little formula to know! 360 ÷ by the exterior angle given = number of sides.
  • Question 8

triangle

Find the value of x

Write your answer in figures without the units.

CORRECT ANSWER
EDDIE SAYS
Sometimes a question presented in this way can make things look more complicated than it is. It's just the same. 360 ÷ 3 = 120° Can you see the connection here? The external angle of a triangle is the same as the sum of the two interior opposite angles.
  • Question 9

Shape A is a 12 sided shape with an exterior angle of 3x.

The exterior angle of shape B is 2x.

external angle algebra

 

CORRECT ANSWER
 36°12°10°12161518
The value of x is
the number of sides shape B has is
EDDIE SAYS
Oh, textbooks and exam papers love this type of questions. But with your knowledge it's okay. Find the exterior angle of shape A first. 360 ÷ 12 = 30° ÷ 3 = 10 x = 10 Shape B the exterior angle = 2 x 10 = 20°: 360 ÷ 20 = 18 sides
  • Question 10

 

What is the exterior angle of an 11 sided shape?

Round your answers to 1 decimal place (1 d.p)

CORRECT ANSWER
EDDIE SAYS
Did you know that the name for an eleven sided shape is a hendecagon? Strange name don't you think? The size of the angle is 360 ÷ 11 = 32.7°
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