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Find Angles Using Knowledge of Sectors

In this worksheet, students will use their knowledge of sectors to find angles when given an arc length and sector area.

'Find Angles Using Knowledge of Sectors ' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

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

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Area Calculations

Popular topics:   Angles worksheets, Geometry worksheets

Difficulty level:  

Worksheet Overview

meat pie


So, you'd like the biggest piece of pie, but have been told you can only have it if you can calculate the angle of it.

That is so unfair. The things you have to do!


As ever, there is a formula to do this.

As we are looking at part of a circle,  is involved of course!


To find the area of a circle we use the formula: πr² or (π x r x r)


It makes sense to use this to help us to find the angle of a sector.

Remember that you can use the π button on your calculator or use the value 3.14




pie chart


The area of the dark blue sector of this pie chart is 25 cm²

The radius is 10 cm.

Find the angle at the centre of this sector.


Angle = (Area x 360) ÷ (π x r x r)

 25 x 360 = 9 000

3.14 x 10 x 10 = 314

9 000 ÷ 314 = 28.7°  (correct to 1 decimal place)


Just follow the steps of the formula carefully and you can't go wrong!


In the following questions, 3.14 has been used as the value of π

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