IGCSEMathsCambridge (CIE)International MathsCoreRevision NotesGeometryBasic Angle PropertiesAngles in Quadrilaterals

Angles in Quadrilaterals (Cambridge (CIE) IGCSE International Maths)

Revision Note

Jamie Wood

Expertise

Maths

Angles in Quadrilaterals

What are the angle properties of quadrilaterals?

  • The four interior angles inside any quadrilateral add up to 360°

  • If the quadrilateral is a square or a rectangle then all the angles are equal to 90°

  • You can use any symmetries of the quadrilateral to identify other equal angles

    • For a parallelogram or rhombus, opposite angles are equal

    • For a kite, one pair of opposite angles are equal

Angle properties of quadrilaterals

Exam Tip

  • Find all the missing angles that you can using the angles that are given to you in a question

    • They might not seem to help you straight away but having more angles will lead you to find the angle you need

Worked Example

The diagram below shows an irregular quadrilateral. Find the value of y.

Quadrilateral angle properties worked example question

Find the missing angle inside the quadrilateral using the rule 'angles in a quadrilateral add up to 360°

First, add together the three given angles

97 space plus space 115 space plus space 85 space equals space 297

Subtract the answer from 360°

table row cell 360 space minus space 297 space end cell equals cell space 63 space end cell end table

Add this to the diagram

Quadrilateral angle properties worked example working

Angles on a straight line add up to 180°, so subtract the answer from 180°

table row cell y plus 63 end cell equals 180 row y equals cell 180 minus 63 end cell row y equals 117 end table

bold italic y bold space bold equals bold space bold 117

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    Jamie Wood

    Author: Jamie Wood

    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.