Angles in Quadrilaterals (Edexcel IGCSE Maths)

Spec point — 4.2B

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

Exam Hint 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 $y$.

Answer:

First, add together the three given angles

$97+115+85=297$

Subtract the answer from 360°

$\begin{gathered} 360 - 297 & = 63 \end{gathered}$

Add this to the diagram

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

$\begin{gathered} y + 63 & = 180 \\ y = 180 - 63 \\ y = 117 \end{gathered}$

$y=117$