The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Understand and Calculate Missing Angles Using Known Angle Facts

In this worksheet, students will be asked to find the missing angles in a shape or around a point using known angle facts.

'Understand and Calculate Missing Angles Using Known Angle Facts' worksheet

Key stage:  KS 2

Curriculum topic:   Exam-style Questions: SATs Maths

Curriculum subtopic:   Exam-Style Questions: Using Known Facts

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Fantastic effort! You have decided to spend some valuable time practising for your Maths SATs test.

In this activity, we will look at how to find the missing angle in a shape or around a point.

 

How do we find missing angles on a straight line?

 

The angles on a straight line add up to 180°.

To calculate the missing angle on a straight line, take away the known angle from 180°.

 

 

180° - 65° = 115°

 

How do we find missing angles in a full turn?

 

The angles in a full turn up add up to 360°.

To calculate the missing angle in a full turn, take away the known angle from 360°.

 

 

105° + 90° + 25° = 220°

360° - 220° = 140°

 

How do we find missing angles on intersecting lines?

 

All 4 angles will add up to 360°.

Opposite angles on a cross are equal.

 

 

Step 1 (we know the angle opposite 65° is also worth 65° so add these together): 65° + 65° =130°

Step 2 (subtract the total of these 2 angles from 360°): 360° - 130° = 230°.

Step 3 (Divide this total by 2 to find what each of the 2 remaining angles is worth): 230°÷ 2 =115°

 

How do we find missing angles in a triangle?

 

The angles in a triangle always add up to 180°.

To find the missing angle, add together the known angles and subtract from 180°.

 

 

If you are given a triangle like this, but asked to find the missing angle, focus only on the angles given, ignore the other information.

 

57° + 90° = 147°

180° - 147° = 33°

 

How do we find missing angles in a quadrilateral?

 

A quadrilateral is a shape with 4 straight sides, like a square, rhombus, parallelogram, trapezium, rectangle.

The angles in a quadrilateral will add always add up to 360°

To find the missing angle, add together the known angles and then subtract from 360°

                                                     

 

90° + 90° + 40° = 220°

360° - 220° = 140

 

Now we have revised those key facts, time to have a go at some practice questions!

 

 

What is the missing angle worth on this straight line?

120°

90°

95°

100°

What is the missing angle in this triangle worth?

 

 

120°

90°

95°

100°

What is angle X worth around this point?

120°

90°

95°

100°

Can you match the statements with the correct label?

 

children thinking

 

Column A

Column B

Angles on a straight line =
180°
Angles around a point =
180°
Angles in a triangle =
360°
Angles in a quadrilateral =
360°
Angles on intersecting lines =
360°

Here are some intersecting lines.

Can you correctly match the value of angles a, b and c?

 

 

Column A

Column B

a =
125°
b =
55°
c =
125°

What is angle b worth on these intersecting lines?

 

 

Column A

Column B

a =
125°
b =
55°
c =
125°

What are angles a and c worth on these intersecting lines?

Column A

Column B

a =
125°
b =
55°
c =
125°

What is angle x worth in this quadrilateral?

 

Column A

Column B

a =
125°
b =
55°
c =
125°

What is the missing angle on the straight line worth?

 

 

Column A

Column B

a =
125°
b =
55°
c =
125°

Can you calculate angle c?

Column A

Column B

a =
125°
b =
55°
c =
125°
  • Question 1

 

What is the missing angle worth on this straight line?

CORRECT ANSWER
90°
EDDIE SAYS
How did you do on this first question? Did you spot that the missing angle must be worth 90° as the given angle is worth 90°? 180°- 90° = 90°. Remember that 90° is the same as a right angle.
  • Question 2

What is the missing angle in this triangle worth?

 

 

CORRECT ANSWER
EDDIE SAYS
Don't worry if you found that tricky, the more you practice, the easier it gets! 90° + 35° = 125° 180° - 125° = 55° Remember the angles in a triangle will always add up to 180°.
  • Question 3

What is angle X worth around this point?

CORRECT ANSWER
EDDIE SAYS
Great effort! There were 2 stages to complete to find that the missing angle X is worth 102°. Remember that the angles around a point will always add up to 360° 118° + 90° + 50° = 258° 360° - 258° = 102°
  • Question 4

Can you match the statements with the correct label?

 

children thinking

 

CORRECT ANSWER

Column A

Column B

Angles on a straight line =
180°
Angles around a point =
360°
Angles in a triangle =
180°
Angles in a quadrilateral =
360°
Angles on intersecting lines =
360°
EDDIE SAYS
Did you get the hang of this one? There was a lot to think about and match but once you know these rules, it really does make finding missing angles so much easier! Keep going- you are making super progress!
  • Question 5

Here are some intersecting lines.

Can you correctly match the value of angles a, b and c?

 

 

CORRECT ANSWER

Column A

Column B

a =
125°
b =
55°
c =
125°
EDDIE SAYS
Phew, that was a toughie! When working out the angles on intersecting lines, remember that opposite angles are equal. So, straight away, we know that angle b = 55° Next, we add 55° + 55° = 110° Subtract this from the total of 360° 360° - 110° = 250° Finally, divide 250° by 2 to find what the last 2 angles are worth. 250 ÷ 2 = 125° You are now halfway through this activity, keep going!
  • Question 6

What is angle b worth on these intersecting lines?

 

 

CORRECT ANSWER
EDDIE SAYS
How are you doing? On these intersecting lines, angle b is worth 27°. We don't need to do any working out for this question as we know that opposite angles are equal on intersecting lines.
  • Question 7

What are angles a and c worth on these intersecting lines?

CORRECT ANSWER
EDDIE SAYS
Nice job if you wrote 153°. To solve this one, we had to carry out the 3 steps of working out. Step 1 = 27° + 27°= 54° Step 2 = 360° - 54° = 306° Step 3 = 306° ÷ 2 = 153° You're making super progress- keep going now!
  • Question 8

What is angle x worth in this quadrilateral?

 

CORRECT ANSWER
EDDIE SAYS
Take a deep breath, you've got this! The angles in a quadrilateral always add up to 360°. Use the angles we have, add them together and then subtract from 360°. 123° + 96° + 70° = 289° 360° - 289° = 71°
  • Question 9

What is the missing angle on the straight line worth?

 

 

CORRECT ANSWER
EDDIE SAYS
This is a tricky one! Great work if you spotted that the missing angle is 32°. To find the answer we had to firstly add together the angles we had: 78° + 70° = 148° 180° - 148° = 32°
  • Question 10

Can you calculate angle c?

CORRECT ANSWER
EDDIE SAYS
Phew, that was a challenge! Great job if you wrote 40°. To find the angle c, we had to remember that vertically opposite angles are equal. So, we had to subtract 17° from 57° = 40° Well done! That is another activity completed, keep up the great work!
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.