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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

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Boy with phoneLost 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 all you need to know for now anyway.

 

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.

Write your answer in figures without the units.

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°
24
72
36
15°
60

triangle

Find the value of x

Write your answer in figures without the units.

external angle algebra

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

The exterior angle of shape B is 2x.

 

 36°12°24°12161518
The value of x is
the number of sides shape B has is

What is the exterior angle of an 11 sided shape?

Write your answer in figures without the units.

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

  • Question 1

hexagon

Calculate the size of the exterior angle of this hexagon.

CORRECT ANSWER
40°
EDDIE SAYS
A hexagon has six sides so all we do is 360 ÷ 6 = 60°
  • Question 2

nonagon

 

CORRECT ANSWER
EDDIE SAYS
The exterior angle of this nonagon is 40° because all we do is 360 ÷ 9 = 40° Are you navigating these activities well?
  • Question 3

decagon

Calculate the exterior angle of this shape.

Write your answer in figures without the units.

CORRECT ANSWER
36
EDDIE SAYS
Okay so you weren't given the number of sides. No worries, just 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
120
EDDIE SAYS
Sometimes a question presented in this way can make things look more complicated that it is. It is just the same. 360 & divide; 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

external angle algebra

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

The exterior angle of shape B is 2x.

 

CORRECT ANSWER
 36°12°24°12161518
The value of x is
the number of sides shape B has is
EDDIE SAYS
Oh text books and exam papers love these type of questions. But with your knowledge it is okay. Find the exterior angle of shape A first. 360 ÷ 10 = 36° ÷ 3 = 12 x = 12 Shape B the exterior angle = 2 x 12 = 24°: 360 ÷ 24 = 15 sides
  • Question 10

What is the exterior angle of an 11 sided shape?

Write your answer in figures without the units.

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

CORRECT ANSWER
32.7
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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