Angle Properties

In this unit of work students are introduced to a range of angle properties including angles on a straight line, in a triangle and vertically opposite.  Students are guided to discover each of the angle properties for themselves so they can link them together later on.

This unit takes place in Term 5 of Year 7 and is the prerequisite unit for angles in parallel lines and exterior angles in polygons which students cover in Year 8.

Angle Properties 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 (°)
  • identify:
    • angles at a point and one whole turn total 360°
    • angles at a point on a straight line total 180°
    • other multiples of 90°
  • recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

Key Concepts
  • Protractors have two scales measuring 0° to 180°.  One scale goes clockwise the other anti-clockwise.  Students should always start measuring from the line that goes through 0°.
  • A right-angle is termed perpendicular and is 90°.
  • A straight line is 180°.
  • Angles about a point have a total of 360°.
  • Vertically opposite angles are equal to each other.
  • Angles in a triangle have a sum of 180°.
  • A quadrilateral is made up of two adjoining triangles and therefore has a sum of 360°.

Working mathematically

Develop fluency

  • Use language and properties precisely to analyse 2-D shapes
  • Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

  • Make and test conjectures about patterns and relationships; look for proofs or counter-examples
  • Begin to reason deductively in geometry, including using geometrical constructions

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

Subject Content


  • Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
  • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  • Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

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