Geometry: Properties of Shapes and Angles
Geometry: Properties of Shapes and Angles covers naming and classifying 2D shapes by their sides and angles and 3D shapes by their faces, edges and vertices, and using angle facts such as angles on a straight line summing to 180 degrees to calculate a missing angle.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the names and properties of common 2D shapes (number of sides, whether sides or angles are equal) and common 3D shapes (number of faces, edges and vertices).
- Learn the four key angle facts: a straight line is 180 degrees, a full turn around a point is 360 degrees, the angles in a triangle sum to 180 degrees, and the angles in a quadrilateral sum to 360 degrees.
- To find a missing angle, add together all the angles you already know, then subtract that total from the relevant angle fact (180 or 360 degrees).
- Learn to classify triangles (equilateral, isosceles, scalene, right-angled) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite) by their properties.
- Practise using a protractor to measure and draw angles accurately, reading from the correct scale.
- Check a calculated angle is a sensible size for the shape described, for example not more than 180 degrees for an angle you expect to be acute or obtuse.
Worked example
Two angles on a straight line are 58 degrees and 47 degrees. A third angle, x, is also on the same straight line. Work out the value of x.
- Recall that angles on a straight line sum to 180 degrees.
- Add the two known angles together: 58 + 47 = 105.
- Subtract this total from 180: 180 - 105 = 75.
- So x = 75 degrees.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1How many sides does a hexagon have?Show answer
Answer: 6
Q2How many faces does a cube have?Show answer
Answer: 6
Q3What type of triangle has all three sides equal?Show answer
Answer: An equilateral triangle
Q4Two angles around a point are 145 degrees and 110 degrees. A third angle completes the full turn. What is its size?Show answer
Answer: 105 degrees (360 - 145 - 110)
Q5A quadrilateral has three angles of 90, 90 and 60 degrees. What is the fourth angle?Show answer
Answer: 120 degrees (360 - 90 - 90 - 60)
Q6Name a quadrilateral with exactly one pair of parallel sides.Show answer
Answer: A trapezium
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A triangle has angles of 42 degrees and 65 degrees. Work out the size of the third angle.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A straight line is split into three angles: 90 degrees, 2x degrees and x degrees. Work out the value of x.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the geometry: properties of shapes and angles worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
Next topics
Not quite what you needed?
Tell us what is missing on geometry: properties of shapes and angles, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.