11+ Maths: Angles in Quadrilaterals
26 October 2026
Angles in quadrilaterals
A quadrilateral is any shape with four sides and four angles. These include squares, rectangles, parallelograms, rhombuses, trapeziums and kites.
Understanding angles in quadrilaterals is important for the 11+ exam because these questions test both shape knowledge and logical reasoning.
Why angles in quadrilaterals matter
The sum of the interior angles in any quadrilateral is always 360 degrees. This fact helps children find missing angles when only some angles are given.
Key insight: Knowing that all four angles add up to 360 degrees allows your child to solve a wide range of geometry problems in the 11+ exam.
Finding a missing angle
If you know three of the angles in a quadrilateral, you can always work out the fourth by subtracting their total from 360.
This method works for all types of quadrilaterals, whether they are regular (like a square) or irregular.
Worked example
A quadrilateral has three angles: 95°, 85° and 110°. What is the size of the fourth angle?
First, add the known angles: 95 + 85 = 180
Then add 110: 180 + 110 = 290
Subtract this total from 360: 360 - 290 = 70
The missing angle is 70 degrees.
Supporting your child
Encourage your child to practise adding the known angles and subtracting from 360. Remind them to check their calculations and to look for any patterns, such as pairs of equal angles in shapes like rectangles and parallelograms.
Regular practice with different types of quadrilaterals builds confidence for the 11+.
