If you want to know more about shape angles you are in the right place! Read the information below, download a free shape angles guide, a free maths angles poster and read our 2D shape blog for more information about 2D shapes.
Important Angles Vocabulary
An angle is the size of the turn between two sides at a vertex. Angles are measured in degrees using a protractor.
An acute angle is an angle that is larger than 90º but smaller than 180º.
A right angle is 90º. Right angles are formed when two lines that are perpendicular to each intersect. For example, squares have four right angles.
An obtuse angle is an angle that is larger than 90º but smaller than 180º.
A straight angle is an angle that is 180º. A straight angle is a point on a straight line.
A reflex angle is an angle that is larger than 180º but smaller than 360º.
A complete angle is an angle that measures 360º. It is the full turn around a point.
The interior angles are the angles inside the lines of a shape.
The exterior angles are the angles outside the lines of a shape.
Angles in polygons
The exterior angles in a polygon always equal 360º
The interior angles of a triangle always equal 180º
The interior angles of a quadrilateral always equal 360º
The interior angles of a pentagon always equal 540º
The interior angles of a hexagon always equal 720º
The interior angles of a heptagon always equal 900º
The interior angles of an octagon always equal 1080º
Formula to work out the interior angles of polygons
The total size of a shape’s interior angles can be worked out using the formula (n - 2) x 180 where n equals the number of sides.
A square has 4 sides so n = 4
(n - 2) x 180
= (4 - 2) x 180
= 2 x 180
A hexagon has 6 sides so n = 6
(n - 2) x 180
= (6 - 2) x 180
= 4 x 180
A nonagon has 9 sides so n = 9
(n - 2) x 180
= (9 - 2) x 180
= 7 x 180
When are angles taught in the Maths National Curriculum?
Angles are taught as part of the geometry strands of the maths curriculum. These strands are geometry - position and direction and geometry - properties of shapes.
Angles are first taught in year 2 when children:
- use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise).
In Year 3 children are taught to:
- recognise angles as a property of shape or a description of a turn
- identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
- identify horizontal and vertical lines and pairs of perpendicular and parallel lines.
All of these objectives are taught in our ready-to-teach Shapes and Angles scheme of work.
In Year 4 children learn to:
This objective is taught in our downloadable Shape Angles scheme of work.
In Year 5 children learn to:
- know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
- draw given angles, and measure them in degrees (º)
- angles at a point and one whole turn (total 360)º)
- angles at a point on a straight line and a turn (total 180º)
- other multiples of 90º
- use the properties of rectangles to deduce related facts and find missing lengths and angles
- distinguish between regular and irregular polygons based on reasoning about equal sides and angles.
In Year 6 children are taught to:
- draw 2-D shapes using given dimensions and angles
- recognise, describe and build simple 3-D shapes, including making nets
- compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
- recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.