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Calculate Interior and Supplementary Angles

In this worksheet, students will learn how to recognise supplementary and interior angles and use the key facts relating to them to find the value of unknown angles and solve related problems.

'Calculate Interior and Supplementary Angles' 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

Cartoon image of a girl with questioning thoughts

 

Question: What do triangles and angles on a straight line have in common?

 

Answer: Angles in a triangle and angles on a straight line always add up to 180°.

 

 

Here is a further fact relating to angles and straight lines:

interior angles example

Interior angles are found within parallel lines, on the same side of the transversal (or the line drawn through them).

 

These angles are sometimes called co-interior or supplementary angles, and we need to be prepared to recognise them by any of these names. 

 

 

There are very few numbers which have great significance in maths, but 180 is definitely one of them!

Great stuff - three facts for the price of one!

 

To calculate a missing interior angle, we just need to subtract the angle given from 180°.

 

 

 

 

Let's put this knowledge of supplementary and interior angles into action now. 

 

In this activity, we will learn how to recognise all types of supplementary and interior angles and use the key fact, that interior angles add up to 180°, to find the value of unknown angles and solve related problems. 

Explore the unknown angles on the diagram below labelled with letters:

 

Diagram showing multiple unknown angles around a pair of parallel lines

Which pairs of angles are interior angles?

h and d

g and h

g and c

a and b

Review the known and unknown angles on this new diagram:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of angle x?

h and d

g and h

g and c

a and b

Observe the known and unknown angles on the diagram below:

Diagram showing known and unknown angles around a pair of parallel lines

Then select the correct answer to complete the expression below. 

 

 61°71°81°
The value of x is...

Explore the known and unknown angles on the diagram below:

Diagram showing known and unknown angles around a pair of parallel lines

Now type a number to complete the statement below. 

 61°71°81°
The value of x is...

Next, review the known and unknown angles on this new diagram:

Diagram showing known and unknown angles around a pair of parallel lines

Then select the correct answers to complete the expressions below. 

 

 216°180°144°134°
Interior angles add up to...
The value of y is...

Investigate the known and unknown angles on this next diagram now:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of angle x?

 216°180°144°134°
Interior angles add up to...
The value of y is...

Explore the angles on the diagram below which have been expressed algebraically:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of x?

45°

55°

40°

30°

Review the angles on the diagram below which have been expressed algebraically:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of y?

 

Type your answer to one decimal place

45°

55°

40°

30°

Observe the known and unknown angles on the trapezium below:

Diagram showing known and unknown angles in a trapezium

What are the values of angles a and b?

45°

55°

40°

30°

Investigate the known and unknown angles on this final diagram now:

 

Diagram showing known and unknown angles around two pairs of parallel lines

 

What are the value of angles x and y?

 115°65°80°
Angle x =
Angle y =
  • Question 1

Explore the unknown angles on the diagram below labelled with letters:

 

Diagram showing multiple unknown angles around a pair of parallel lines

Which pairs of angles are interior angles?

CORRECT ANSWER
h and d
g and c
EDDIE SAYS
Sometimes these angles can be tricky to spot if there are several shown in a collection. Consider each pair one at a time, ignoring all other angles in each case. 'Interior' is the clue word here, so we need to look inside the parallel lines. Remember that two angles which are interior will be on the same side of the transversal and will both add up to 180°. The only pairs which show this accurately are h and d, plus g and c. Review the Introduction now before you move on if any of these terms are unfamiliar or you found recognising these pairs of interior angles to be tricky.
  • Question 2

Review the known and unknown angles on this new diagram:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of angle x?

CORRECT ANSWER
EDDIE SAYS
We know that interior angles add up to 180°. So we can take 128° away from 180° and this will give us the value of x: 180° - 128° = 52° Always show your working out in exams, as this is where marks can still be earned even if you reach an incorrect answer accidentally.
  • Question 3

Observe the known and unknown angles on the diagram below:

Diagram showing known and unknown angles around a pair of parallel lines

Then select the correct answer to complete the expression below. 

 

CORRECT ANSWER
 61°71°81°
The value of x is...
EDDIE SAYS
Again, a simple subtraction is all that is required here: 180° - 109° = 71° Have you noticed that interior angles make a C-shape or a backward C-shape within the parallel lines? This may be helpful to remind us that a Calculation is required in this supplementary angle case.
  • Question 4

Explore the known and unknown angles on the diagram below:

Diagram showing known and unknown angles around a pair of parallel lines

Now type a number to complete the statement below. 

CORRECT ANSWER
EDDIE SAYS
Let's subtract again: 180° - 132° = 48° Have you noticed that one angle is obtuse in each pairing, and the other is acute? A quick way to spot an error is if we get two acute or two obtuse angles, then we must have made a mistake somewhere.
  • Question 5

Next, review the known and unknown angles on this new diagram:

Diagram showing known and unknown angles around a pair of parallel lines

Then select the correct answers to complete the expressions below. 

 

CORRECT ANSWER
 216°180°144°134°
Interior angles add up to...
The value of y is...
EDDIE SAYS
All we have to remember is that the interior angles always add up to 180°. In this case: 180° - 36° = 144°
  • Question 6

Investigate the known and unknown angles on this next diagram now:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of angle x?

CORRECT ANSWER
EDDIE SAYS
Are you getting the hang of these now? 180° - 106° = 74° Let's make the next question slightly more challenging then...
  • Question 7

Explore the angles on the diagram below which have been expressed algebraically:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of x?

CORRECT ANSWER
30°
EDDIE SAYS
Oh no... what's this? This time we can see that algebra has been used instead of numbers to express our angles. Don't worry though, we still have all the knowledge that we need to solve this problem. We know that interior angles add up to 180°. Plus, we also know that there are 6x altogether (as 5x + x = 6x). So to find the value of x on its own, we need to share 180 between 6 lots of x: x = 180° ÷ 6 = 30°
  • Question 8

Review the angles on the diagram below which have been expressed algebraically:

Diagram showing known and unknown angles around a pair of parallel lines

What is the value of y?

 

Type your answer to one decimal place

CORRECT ANSWER
EDDIE SAYS
More algebra - bring it on! There are 8y altogether (as 7y + 7 = 8y). So to find the value of y on its own, we need to share 180 between 8 lots of y: y = 180° ÷ 8 = 22.5°
  • Question 9

Observe the known and unknown angles on the trapezium below:

Diagram showing known and unknown angles in a trapezium

What are the values of angles a and b?

CORRECT ANSWER
EDDIE SAYS
Often sneaky examiners will hide an interior angle question within a larger shape, as we can see here. A trapezium has one set of parallel sides. We can see that there are two sets of interior angles within these lines. To find angle a, we need to calculate: 180° - 80° = 100° To find angle b, we need to calculate: 180° - 110° = 70° Job done!
  • Question 10

Investigate the known and unknown angles on this final diagram now:

 

Diagram showing known and unknown angles around two pairs of parallel lines

 

What are the value of angles x and y?

CORRECT ANSWER
 115°65°80°
Angle x =
Angle y =
EDDIE SAYS
Nice try, but one extra line isn't going to confuse us, is it? We can see here that there are two sets of interior angles within two pairs of parallel lines. However, only one calculation is required, as both angles x and y are interior to 65°. So angle x and angle y will be the same. 180° - 65° = 115° Great work! You have learnt how to recognise all types of supplementary and interior angles and use the key fact, that interior angles add up to 180°, to find the value of unknown angles and solve related problems.
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