GCSE MATHS • HIGHER TIER
Angles in the Same Segment Made Simple
Learn how to recognise angles standing on the same chord, apply the equality rule, and solve numerical and algebraic circle-theorem questions.
Clear method
Exam practice
Worked proofs
Angles in the Same Segment in Four Moves
1
Identify
Identify the chord used by both angles.
2
Check
Confirm both angles lie in the same segment.
3
Set Equal
Use the theorem to set the two angles equal.
4
Solve
Find the missing angle or solve the algebra.
What You’ll Learn
Understand the Theorem
Understand why angles in the same segment are equal.
Recognise Chords and Segments
Identify the shared chord and the segment containing the angles.
Apply the Key Rule
Use equal angles to find missing values quickly.
Solve Algebraic Questions
Form equations when angles are written using algebra.
Connect Circle Theorems
Use this theorem alongside other GCSE circle-theorem rules.
Key Rules
Angles in the same segment are equal.
This means that if two angles are formed from the same chord and arc, they must be identical.
Understanding Chords & Segments : A chord is a straight line joining two points on the circumference of a circle. A segment is the region between a chord and the arc connected to it. The theorem only works when both angles lie in the same segment.
Worked Proof: Arc Length
Step-by-Step Method
- 1. Identify the chord.
- 2. Locate the two angles.
- 3. Check that both stand on the same chord.
- 4. Confirm they lie in the same segment.
- 5. Set the angles equal.
- 6. Solve any calculations or algebra.
More Worked Examples
1
Question: One angle in a segment is 72°.
Using the theorem, the matching angle is equal.
2
Question: One angle in a segment is 105°.
The corresponding angle in the same segment must also be 105°.
3
Question: Two angles in the same segment are x and 65°.
x = 65
4
Question: Two angles in the same segment are x + 15 and 90°.
x + 15 = 90
x = 75
x = 75
- Common GCSE Mistakes
- Wrong segment: Check both angles lie in the same segment.
- Wrong theorem: Do not confuse it with Angles at the Centre.
- Missed chord: Identify the shared chord first.
- Algebra errors: Set equal angles correctly before solving.
- Diagram errors: Read the angle positions carefully.
- Exam Tips
- Find the chord first: It is the main clue.
- Check both angles: They must stand on the same chord.
- State the theorem: Name it in reasoning questions.
- Mark equal angles: Add matching marks on the diagram.
- Show algebra clearly: Write the equality before solving.
Skills Used in Angles in the Same Segment
Angles at the Centre
Cyclic Quadrilaterals
Tangent Theorems
Alternate Segment Theorem
Radius and Tangent Theorem
Circle Geometry
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Angles in the Same Segment Tutorial
Step-by-step walkthroughs of Angles in the Same Segment with clear methods and exam tips.
Frequently Asked Questions
Angles in the same segment of a circle are equal.
A chord is a straight line joining two points on the circumference.
A segment is the region between a chord and its corresponding arc.
Look for two angles standing on the same chord and lying in the same segment.
Yes. Set the two equal angles equal to each other and solve the equation.
Angles at the Centre, Cyclic Quadrilaterals, Tangent Theorems, the Alternate Segment Theorem and the Radius and Tangent Theorem.
