IGCSEMathsCambridge (CIE)International MathsCoreRevision NotesGeometryBasic Angle PropertiesAngles around Points & Lines

Angles around Points & Lines (Cambridge (CIE) IGCSE International Maths)

Revision Note

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Cambridge (CIE) International Maths: CoreEdexcel Maths A (Modular): Higher Unit 2Cambridge (CIE) International Maths: Extended

Basic Angle Properties

What are the basic angle properties?

  • Angles around a point add up to 360°

  • Angles that form a straight line add up to 180°

  • Vertically opposite angles are equal

    • Vertically opposite angles occur when two lines intersect, as in the diagram below

Vertically opposite angles

Examiner Tips and Tricks

  • Use the angle properties to find any missing angles that you can, and mark them on the diagram

    • Even if they are not the angle you are trying to find, they may help provide a clue!

Worked Example

The diagram below shows three straight lines intersecting at a point.

Basic angle properties worked example question

Find the values of x and y.

Vertically opposite angles between two intersecting lines are equal

x space equals space 25

Angles that meet on a straight line add up to 180°

table row cell x space plus space y space plus space 98 space end cell equals cell space 180 space end cell row cell 25 space plus space y space plus space 98 space end cell equals cell space 180 end cell row cell 123 space plus space y space end cell equals cell space 180 end cell end table

Solve to find y

y equals 180 minus 123 y equals 57

bold italic x bold space bold equals bold space bold 25 bold space bold comma bold space bold italic y bold space bold equals bold space bold 57

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    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.