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Polygons – WJECInterior and exterior angles

In this WJEC GCSE study guide, you will learn all about quadrilateral angles, shapes, geometry and angles and why they are important areas of mathematics. Read through the mathematics revision guide and learn how to calculate angles of regular and irregular polygons and create tessellations and tiling patterns.

Part of MathsGeometry and Measure

Interior and exterior angles

A polygon is simply a shape with three or more sides and angles. Quadrilaterals are 2D shapes with four sides and angles.

There are six special quadrilaterals with different properties.

Square

A square with dotted lines from corner to corner, showing a right angle where the lines cross.
  • A square has four sides of equal length.
  • It has four right angles (90°).
  • The opposite sides are parallel.
  • The each other at right angles.
  • The exterior angles of a square are each 270°.

Rectangle

A rectangle with dotted lines from corner to corner, showing a right angle in each corner.
  • A rectangle has two pairs of equal sides.
  • It has four right angles (90°).
  • The opposite sides are parallel.
  • The diagonals bisect each other.
  • The exterior angles of a rectangle are each 90°.

Parallelogram

A parallelogram with dotted lines from corner to corner. It has two pairs of equal angles, coloured yellow and green.
  • A parallelogram has two pairs of equal sides.
  • It has two pairs of equal angles.
  • It has two pairs of equal exterior angles.
  • The opposite sides are parallel.
  • The diagonals bisect each other.

Rhombus

A rhombus with dotted lines from corner to corner, showing a right angle where the lines cross.  It has two pairs of equal angles, coloured yellow and green.
  • A rhombus has four sides of equal lengths.
  • It has two pairs of equal angles.
  • It has two pairs of equal exterior angles.
  • The opposite sides are parallel.
  • The diagonals bisect each other at right angles.

Trapezium

A trapezium with one pair of parallel sides.
  • A trapezium has one pair of parallel sides.

Kite

A kite with dotted lines from corner to corner, showing a right angle where the lines cross. It has one pair of equal angles, coloured green.
  • A kite has two pairs of equal sides.
  • It has one pair of equal angles.
  • One diagonal is bisected at right angles by the other.