Angles in Maths Explained – GCSE Maths Revision Guide
An angle is formed when two lines meet at a point. In geometry, angles help us understand the space between these two lines or rays, and they are measured in degrees (°). From building structures to solving puzzles, understanding angles is essential, not just in maths but also in real-life applications.
In this GCSE Maths revision guide, we’ll explain everything you need to know about angles. With real examples, diagrams, and tips, you’ll build a solid understanding that will help you tackle your exams with confidence.
Why Understanding Angles Is Important for GCSE Maths
Angles are a core part of the GCSE Maths syllabus. They’re assessed in geometry, algebra, and trigonometry sections. Whether you’re solving missing angles, working with parallel lines, or analysing shape properties, you’ll need a firm grasp of angle rules.
Key reasons to learn angles:
- They appear in at least 10–15% of your GCSE paper.
- Mastery of angles improves problem-solving skills.
- Helps in understanding real-world structures, design, and patterns.
Types of Angles: Definitions and Examples
Acute Angles
An acute angle measures less than 90°.
Example: A triangle with angles of 40°, 60°, and 80° has all acute angles.
Right Angles
A right angle is exactly 90°.
Symbol: A small square is used to indicate it.
Example: The corners of a square or rectangle.
Obtuse Angles
An obtuse angle is greater than 90° but less than 180°.
Example: A 120° angle in a kite.
Straight Angles
A straight angle is exactly 180°, forming a straight line.
Example: A ruler laid flat shows a straight angle.
Reflex Angles
A reflex angle is more than 180° but less than 360°.
Example: An angle of 270° in a full turn.
Angle Properties in Geometric Shapes
Angles in a Triangle
- The interior angles of any triangle add up to 180°.
- Types of triangles based on angles:
- Acute-angled triangle: all angles < 90°
- Right-angled triangle: one angle = 90°
- Obtuse-angled triangle: one angle > 90°
Angles in a Quadrilateral
- The interior angles of a quadrilateral add up to 360°.
Examples:- Square: 4 right angles (4 × 90° = 360°)
- Trapezium or parallelogram: angle pairs are supplementary
Angle Facts You Must Memorise
Here’s a table of essential angle facts:
| Angle Rule | Value |
| Angles on a straight line | 180° |
| Angles around a point | 360° |
| Vertically opposite angles | Equal |
| Base angles of an isosceles triangle | Equal |
| Interior angles in a triangle | 180° |
| Interior angles in a quadrilateral | 360° |
| Alternate angles (Z-angle rule) | Equal |
| Corresponding angles (F-angle rule) | Equal |
| Co-interior (same side) angles (C-angle rule) | Add up to 180° |
Calculating Missing Angles: Step-by-Step Methods
You will often be asked to find a missing angle using known rules.
Example 1:
Find the missing angle on a straight line if one is 135°.
Solution: 180° – 135° = 45°
Example 2:
In a triangle with angles 50° and 60°, find the third angle.
Solution: 180° – (50° + 60°) = 70°
Example 3:
Given vertically opposite angles where one is 110°, the other is also 110°.
Common Angle Mistakes in GCSE Exams (And How to Avoid Them)
- Using the wrong protractor scale: Always check if you’re starting at 0° or 180°.
- Forgetting angle sum rules: Memorise triangle (180°) and straight line (180°) facts.
- Misreading Z/F/C angles in diagrams: Practise identifying angle relationships in complex diagrams.
- Poor working out: Always show clear steps – you may still receive method marks even if the answer is incorrect.
GCSE Practice Questions with Solutions
Question 1
A triangle has angles of 45° and 65°. Find the third angle.
Answer: 180° – (45° + 65°) = 70°
Question 2
Find the missing angle on a straight line if one is 138°.
Answer: 180° – 138° = 42°
Question 3
If two corresponding angles are given as 70° and x, find x.
Answer: x = 70° (corresponding angles are equal)
Conclusion
Angles are a building block of GCSE Maths. By understanding their types, properties, and the rules they follow in various shapes and diagrams, you can solve even the trickiest geometry questions. Practise regularly, apply the rules consistently, and always show your working. Enrol for affordable Online GCSE Courses
FAQs About Angles in Maths
1. What is an angle in simple terms?
An angle is the space between two lines that meet at a point, measured in degrees.
2. What is the sum of angles in a triangle?
The total interior angle sum in a triangle is always 180°.
3. What are corresponding angles?
They appear on the same side of a transversal line across two parallel lines and are equal.
4. What is a reflex angle?
An angle greater than 180° but less than 360°.
5. How do I measure an angle with a protractor?
Align the base with one side of the angle, place the midpoint on the vertex, and read the correct scale.