Where can I download free angles PDF worksheets with answers?

On this MathsLinks page you can download free printable angles PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), Ken Stafford (2), Maths Genie, Corbett Practice, plus a printable one-page angles revision guide.

What GCSE grade is angles (2K)?

Angles (topic code 2K) is a Grade 2 geometry topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Angles Worksheets (PDF) with Answers — GCSE Maths

Free Angles PDF Worksheets & Answers

Grade 2 • Topic 2K

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
Ken Stafford (2) Practice worksheet & worked solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Dr Frost (B. Blocks) Building Blocks skill sheet & answers	Qs	Ans
Maths4EveryOne KS2 SATs questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
GCSE Maths Rocket (1) Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page

Grade 2 topics
2A - Calculation problems	2B - Using a calculator
2C - Systematic listing	2D - Fraction of an amount
2E - FDP	2F - Simplifying algebra
2G - Writing an expression	2H - Function machines
2J - Solving one step equations	2K - Angles
2L - Area and perimeter	2M - Reading scales
2N - Probability & Probability Scale	2P - Frequency polygons
2Q - Unitary method	2R - Bar charts
2S - Pie charts	2T - Averages
2U - Stem and leaf diagrams

Explanation:

Memorise the five core angle facts and their exact wording for “give a reason” questions: (1) Angles on a straight line add up to 180°; (2) Angles around a point add up to 360°; (3) Vertically opposite angles are equal; (4) Angles in a triangle add up to 180°; and (5) Angles in a quadrilateral add up to 360°.

In an isosceles triangle, the two equal sides are marked with tick marks, and the base angles opposite those equal sides are equal.

Example 1: Find the size of angle x on the straight line below.

• Angles on a straight line add up to 180°:

• 48° + 65° = 113° → x = 180° − 113° = 67°

Example 2: An isosceles triangle has a top angle of 46° between its two equal sides. Find the base angle y.

• Remaining angle sum: 180° − 46° = 134°

• Base angles are equal: y = 134° ÷ 2 = 67°

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Angles Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Jun 2025 2F Q9 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

PQR is a straight line.

(i) Work out the value of x. [2 marks]

(ii) Give a reason for your answer. [1 mark]

Worked Solution & Mark Scheme (3 marks)

Part (i) Solution:

x = 180 – 85 – 30 = 65 M1 A1

Answer (i): x = 65

Part (ii) Solution:

Angles on a straight line add up to 180°

Answer (ii): Angles on a straight line add up to 180°

Past Paper Example 2 GCSE Nov 2022 3F Q13 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

ABCD is a quadrilateral.

(a) Work out the size of angle x. [1 mark]

Give a reason for your answer. [1 mark]

(b) The diagram is wrong.
Explain why. [1 mark]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

360 – (120 + 120 + 80) = 40° B1

Answer (a): 40

Part Solution:

Angles in a quadrilateral add up to 360°

Answer : Angles in a quadrilateral add up to 360°

Part (b) Solution:

80 + 60 + 50 = 190° C1

Answer (b): Angles in a triangle add up to 180°, but 80 + 60 + 50 = 190°

Past Paper Example 3 AQA Jun 2019 3F Q10 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

In rectangle ABCD
triangle ABE is equilateral
triangle CDE is isosceles, with CE = DE

Work out the size of angle x.

Worked Solution & Mark Scheme (4 marks)

In equilateral triangle ABE, each angle is 60°, so ∠ AEB = 60° M1
In isosceles triangle CDE, ∠ EDC = 65°, so ∠ ECD = 65°
Therefore, ∠ DEC = 180° - (65° + 65°) = 50° M1
By symmetry, ∠ AED = ∠ BEC = x
The angles around point E sum to 360°: M1
∠ AEB + ∠ BEC + ∠ DEC + ∠ AED = 360°
60° + x + 50° + x = 360°
2x + 110° = 360° ⇒ 2x = 250° ⇒ x = 125°. A1

Answer: Answer 125 degrees

← 2J Solving one step equations

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Angles

Free Angles PDF Worksheets & Answers

Guide to Angles: Explanation, Diagrams & Worked Examples

GCSE Past Paper Angles Questions & Answers