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Apply Cyclic Quadrilateral Theorem

In this worksheet, students will find the value of unknown angles and solve problems requiring the application of the theory that opposite angles in a cyclic quadrilateral total 180°.

'Apply Cyclic Quadrilateral Theorem' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

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

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions Circles

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Question: Why does nobody talk to circles?

 

Because there is no point!

 

But within one particular circle theorem, there are points in a circle in the shape of a quadrilateral.

This circle theorem is known as angles in a cyclic quadrilateral.

 

 

Let's investigate this theory in action now...

 

The sum of the opposite angles in a cyclic quadrilateral add up to 180°. 

 

Cyclic quadrilateral diagram 1

 

So in the diagram above, a + d = 180° and b + c = 180°.

 

 

For example, in the diagram below the opposite angles add up to 180°:

 

Cyclic quadrilateral diagram 2

 

76 + 104 = 180°

92 + 88 = 180°

 

 

By extension, this means that the total angles in a quadrilateral will add up to 360°.

 

But, be careful!

 

Danger sign The quadrilateral must fill the circle (i.e. each of its four corners must touch the circumference) or it cannot be classed as a cyclic quadrilateral. 

 

 

In this activity, we will find the value of unknown angles and solve problems requiring the application of the theory explained above. 

As ever in circle and angle investigations, we will be asked to recall other angle properties too.

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