GCSE MATHS • HIGHER TIER
Angles Around a Point Made Simple
Use the 360° full-turn rule to find missing angles and solve numerical and algebraic GCSE geometry questions.
Clear method
Exam practice
Worked proofs
Angles Around a Point in Four Moves
1
Identify
Identify the single point where all the angles meet.
2
Write
Write angles around a point = 360°.
3
Calculate
Add the known angles and solve any algebra.
4
Check
Add all angles to confirm the total is 360°.
What You’ll Learn
Use the 360° Rule
Know that angles around one point total 360°.
Find Missing Angles
Subtract known angles from a full turn.
Solve Algebraic Angles
Form and solve equations involving x and angle expressions.
Avoid Rule Confusion
Distinguish angles around a point from angles on a straight line.
Apply Exam Technique
Show the correct angle fact and check the final total.
Key Rules
Angles around a point = 360°
Angles around a point always add up to 360°. If several angles meet at a single point, their total must equal 360°.
Why Does the Rule Work?
A complete turn around a point forms a full circle. A full circle contains 360°. Therefore, all angles meeting at that point must add to 360°.
Worked Proof: Angles Around a Point
Visual Understanding
Imagine standing in one spot and turning all the way around until you face the same direction again. You have completed a 360° turn. Any angles around that point must therefore total 360°.
More Worked Examples
1
One angle is 120° and another is 140°. Find the missing angle.
Step 1: Add known angles.
120 + 140 = 260
Step 2: Subtract from 360
360 - 260 = 100
Step 2: Subtract from 360
360 - 260 = 100
2
Three angles around a point are 80°, 90° and 70°. Find the missing angle.
80 + 90 + 70 = 240
360 - 240 = 120
3
Angles are x, 110° and 90°
x + 110 + 90 = 360
x + 200 = 360
x = 160
x = 160
4
Angles are 2x, 100° and 80°
2x + 100 + 80 = 360
2x + 180 = 360
2x = 180
x = 90
2x = 180
x = 90
- Common GCSE Mistakes
- Wrong total: Use 360° around a point, not 180°.
- Missing an angle: Include every angle meeting at the point.
- Algebra errors: Simplify and solve equations carefully.
- Arithmetic errors: Check addition and subtraction.
- Diagram misread: Confirm the angles form a complete turn.
- Exam Tips
- Write the angle fact first: Angles around a point = 360°.
- Add known angles carefully: Then subtract from 360°.
- For algebra, form one equation: Set the full sum equal to 360°.
- Compare with a straight line: Use 180° only when the diagram shows a straight line.
- Check by adding everything: The final total must be 360°.
Skills Used in Angles Around a Point
Angle Facts
Arithmetic
Algebra
Angles on a Line
Vertically Opposite Angles
Parallel Lines
Polygon Angles
Geometry Problem Solving
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Printable Worksheet
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Interactive Quiz
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Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Angles Around a Point Tutorial
Step-by-step walkthroughs of Angles Around a Point with clear methods and exam tips.
Frequently Asked Questions
They always add up to 360°.
A complete turn forms a full circle, which contains 360°.
Add the known angles and subtract their total from 360°.
Add all angle expressions, set the total equal to 360°, and solve the equation.
Angles on a straight line total 180°, while angles around a point total 360°.
Add all angles together and confirm the total is 360°.