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Use Angle Properties in a Triangle

In this worksheet, students will use the key fact, that angles in a triangle always add to 180°, to find the value of unknown angles in triangles and identify triangles accurately.

'Use Angle Properties in a Triangle ' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

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

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions Angles

Difficulty level:  

Worksheet Overview

Illustration of the pyramids in EgyptPhoto of a musical triangleImage of the fire triangle


Oh yes, the humble triangle, we take it for granted.

Its shape has been used by Egyptian kings, musicians and in warning signs, to name just a few of its many uses!


There are lots of properties (facts) about triangles that people have learned over the centuries, and now it is your turn.



 Special Triangles


Diagram of special types of triangles


 Diagram of positions of right angles in triangles


We need to look out for the markings on these triangles, as these quite often tell us which type of triangle we are looking at.

e.g. A triangle marked |||, || and | on the sides show that each side and angle is different, so therefore it must be scalene.

e.g. The two red angles in the isosceles triangle, highlight the base angles which are the same.



A Key Triangle Fact:

Angles in a triangle always add up to 180°.



Using this knowledge, we can find missing angles in a triangle.

Let's look at how we can do this now. 




e.g. What is the value of angle f in the first triangle below? And the value of angles a and b in the second triangle?


Diagram of finding a missing angle in an isosceles triangle


From the markings on these triangles, we can see these are both isosceles triangles.

As a result, we know that the base angles must be the same.




e.g. What is the value of angle b in the diagram below? 


Diagram of finding an external angle of a triangle


Here, we have been asked to find an angle that is external to the triangle.


We need to put two rules we know together here - if we extend the base of the triangle we have a straight line.

What facts do we know about straight lines?


The angles on a straight line will also add up to 180°, so we can use this fact to find the missing exterior angle. 




Right then, let's put what we know into action now. 


In this activity, we will use the key fact, that angles in a triangle always add to 180°, to find the value of unknown angles in triangles, identify triangles accurately and solve problems involving triangles. 

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