Angle Facts
Get to grips with angle facts using these Foundation GCSE Maths practice questions. The worksheet focuses on using basic angle facts, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Angles on a straight line add to 180°; angles around a point add to 360°.
Free downloads
These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
A small set of angle facts solves most missing-angle problems. Angles on a straight line add to \(180^\circ\), angles around a point add to \(360^\circ\), and vertically opposite angles are equal.
These combine with the triangle and quadrilateral rules to handle almost any diagram. The skill is spotting which fact applies, which usually means looking for a straight line, a full turn, or a crossing point.
Exam questions almost always ask for a reason as well as a value. Writing angles on a straight line add to 180 degrees earns a mark in its own right, so the reason should be stated every time.
Revision notes
The three core facts
Angles on a straight line sum to \(180^\circ\). Angles around a point sum to \(360^\circ\). Vertically opposite angles, formed where two lines cross, are equal.
Each has a standard wording, and using that wording is what earns the reasoning mark.
Working through a diagram
Find any angle you can, mark it on the diagram, then use it to find the next.
Working in steps and labelling as you go turns a complicated diagram into a series of one-step problems.
Giving reasons
State the fact you used for each step, not just the arithmetic.
A full answer reads: \(x = 180 - 65 = 115^\circ\), because angles on a straight line add to \(180^\circ\).
Key points
- Angles on a straight line add to \(180^\circ\).
- Angles around a point add to \(360^\circ\).
- Vertically opposite angles are equal.
- Mark each angle on the diagram as you find it.
- Always give a reason with each step.
- Use the standard wording for reasons.
Worked examples
Example 1
Two angles on a straight line are \(x\) and \(112^\circ\). Find \(x\).
Working
Example 2
Three angles around a point are \(140^\circ\), \(95^\circ\) and \(y\). Find \(y\).
Working
Example 3
Two lines cross. One angle is \(47^\circ\). Find the vertically opposite angle.
Working
Common mistakes
Not giving a reason.
The reason is worth a mark on its own, so state the fact every time.
Using 360 where 180 applies.
A straight line is 180 degrees; a full turn around a point is 360.
Assuming a diagram is drawn to scale.
Diagrams are usually not accurate, so calculate rather than measure.
Confusing vertically opposite with adjacent angles.
Vertically opposite angles are across the crossing point from each other, and are equal.
Exam tips
- Mark every angle you find on the diagram.
- Write the reason alongside each calculation.
- Work in small steps rather than trying to see the whole answer at once.
- Check your answer against the type of angle shown.
Key terms
- Vertically opposite
- Angles across from each other where two lines cross.
- Adjacent
- Next to each other, sharing an arm.
- Straight line
- A line making an angle of \(180^\circ\).
- Reason
- The stated fact justifying a calculation.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.