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Solve Problems Involving Parallel Lines

In this worksheet, students will combine their knowledge of angle properties and parallel lines to solve problems which involve taking multiple steps to calculate unknown angles using number and algebra.

'Solve Problems Involving Parallel Lines' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, AQA, Eduqas, OCR,

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions Angles

Difficulty level:  

Worksheet Overview

Parallel lines have so much in common - it's a shame they will never meet!

parallel lines

Engineers, architects and designers all need to know and use key facts about angles and straight lines in their work - we wouldn't want a wonky house or an aircraft with uneven wings, would we? 

 

 

Knowing the properties (facts) of angles and parallel lines can help us to solve all sorts of problems.

 

Let's remind ourselves of the key facts now...

Diagram of angles around a point

 

 

Angles on a straight line add up to 180°:

Diagram showing examples of interior angles

 

Alternate angles (or Z-angles) are equal:

Diagram showing example of alternate angles

 

 

Corresponding angles (or F-angles) are also equal:

Diagram showing examples of corresponding angles

 

Often we will see more than one of these rules in action within the same problem, so we need to have our eagle eyes ready to spot these scenarios.

 

Lets give this a go now in some examples. 

 

 

 

e.g. Find the value of angle x in the diagram below:

Diagram showing angles between two parallel lines with one missing

Here, we need to draw another parallel line through the centre of our diagram to help. 

Don't worry, there are no rules to say that we can't do this!

Diagram showing angles between two parallel lines with one missing

This has split our target angle (x) into two elements.

We can now apply the alternate angle rule from above to link these two elements to the angles already provided:

x = 28° + 38° = 66°

 

 

 

 

e.g. Find the value of x and y in the diagram below:

Diagram showing angles between two parallel lines with two missing

Angle y is a corresponding angle to 114° so these must have the same value

 

Angle x and y are on a straight line, so together will add up to 180°. 

Therefore, x = 180° - 114° = 66°

 

 

Now we are going to put all the rules we know relating to angles and straight lines together to solve problems which involve taking multiple steps to calculate unknown angles using number and algebra. 

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