Angle Properties

Students learn how to draw, measure and identify different types of angles.  They use this knowledge to discover various angle properties such as angles on a straight line, about a point, in a triangle and on parallel lines.  As learning progress they are challenged to construct polygons and solve problems involving their interior and exterior angles.  Angle properties is studied in Term 6, Year 9  of the Foundation GCSE course and follows Properties of 2D shapes.

Angle Properties Lessons
Revision Lessons

Prerequisite Knowledge

  • Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
  • draw given angles, and measure them in degrees (°)


  • angles at a point and one whole turn (total 360°)
  • angles at a point on a straight line and 1/2 a turn (total 180°)
  • other multiples of 90°

Success Criteria

  • use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries;
  • use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description
  • apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles;
  • understand and use alternate and corresponding angles on parallel lines;
  • derive and use the sum of angles in a triangle (e.g. to deduce use the angle sum in any polygon, and to derive properties of regular polygons)

Key Concepts

  • Understanding the basic angle properties such as the types of angles helps students with angle measurements.
  • Rather than being told (or given) angle properties students should have the opportunity to discover and make sense of them practically.
  • Use the Geogebra files to demonstrate the angle properties.
  • Geometric problems can often be solved using various angle properties. Encourage students to look for alternative properties.
  • Demonstrate how a polygon is made up from interior triangles when calculating their angles.

Common Misconceptions

  • When measuring angles using a 180° degree protractor students often confuse the upper and lower scale. Understanding basic angle properties such as acute and reflex angles helps with this.
  • Students often forget the definition of properties associated to angles in parallel lines.
  • Exterior angles in a polygon have to travel in the same direction for the sum to be 360°.

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