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

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°.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Showing Progress during a Mathematics Lesson

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]

Plotting and Interpreting Conversion Graphs

Plotting and interpreting conversion graphs requires linking together several mathematical techniques.  Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs.  These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]

Calculating the Volume of a Pyramid

When calculating the volume of a pyramid we can substitute the values of the length, width and perpendicular height into the formula V = 1/3 lwh.  In my experience this is often provided for the students with little explanation as to why a volume of a pyramid is exactly one third the volume of a […]