Angles
Measuring and calculating angles, including angles on a straight line, at a point, in triangles and quadrilaterals.
What is Angles?
An angle is a measure of turn between two lines that meet at a point. Angles are measured in degrees. In the 11+ exam, you need to know angle types, angle rules and how to calculate missing angles.
The key angle facts are: angles on a straight line add up to 180 degrees, angles at a point add up to 360 degrees, angles in a triangle add up to 180 degrees, and angles in a quadrilateral add up to 360 degrees.
Step-by-Step Method
Identify the angle type
Acute (less than 90), right angle (exactly 90), obtuse (between 90 and 180), reflex (between 180 and 360).
Identify which angle rule applies
Look for straight lines (180), full turns (360), triangles (180), quadrilaterals (360), or vertically opposite angles (equal).
Write an equation
Add all the angles together and set them equal to the total (180 or 360).
Solve for the missing angle
Subtract the known angles from the total.
Check your answer is sensible
Does the missing angle look about right compared to the diagram? An obtuse angle should be more than 90.
Worked Examples
Two angles on a straight line are 115 degrees and x. Find x.
Working
- Angles on a straight line = 180 degrees.
- x = 180 – 115 = 65 degrees.
A triangle has angles of 40 degrees and 75 degrees. Find the third angle.
Working
- Angles in a triangle = 180 degrees.
- Third angle = 180 – 40 – 75 = 65 degrees.
Two straight lines cross. One angle is 130 degrees. Find the angle opposite it.
Working
- Vertically opposite angles are equal.
- The opposite angle = 130 degrees.
- The other two angles = 180 – 130 = 50 degrees each.
Common Mistakes
Using 360 for a triangle instead of 180.
Angles in a TRIANGLE = 180. Angles in a QUADRILATERAL = 360. Angles at a POINT = 360.
Forgetting that vertically opposite angles are equal.
When two straight lines cross, the opposite angles are always equal.
Estimating from the diagram instead of calculating.
Diagrams are often NOT drawn to scale. Always calculate using angle rules.
Top Tips
- Learn the four key facts: straight line = 180, point = 360, triangle = 180, quadrilateral = 360.
- Vertically opposite angles are always equal – this is a very common exam question.
- If a question has parallel lines, look for alternate angles (Z-angles) and corresponding angles (F-angles).
- Always show your working and state which angle rule you are using.
Ready to practise?
Put these techniques into action with our free practice papers.
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