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Angles in polygons

Angles in polygons for GCSE Statistics OCR Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • OCR
  • Statistics
  • Foundation
  • Spec A16 · A8 · A11
  • 5 min read
  • 9 revision boxes

Introduction

2 boxes
2 min read

What is angles in polygons?

Listen to this box

Transcript

A short spoken summary of angles in polygons and where it is used.

A spoken walk-through of angles in polygons before you read the notes.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing angles in polygons laid out step by step

The same idea drawn out, so the method is visible.
5 rows

The angles in polygons reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 1 column 4
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 2 column 4
Row 3 column 1
Row 3 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 4

Learning

5 boxes
5 steps

How to work with angles in polygons

The examiner marks the working, so a correct answer with no method still drops marks.
The layout below is the one the mark scheme expects.

Diagram showing angles in polygons laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for angles in polygons in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Angles in polygons

This idea appears again in the higher-mark questions, so it is worth over-learning.

  • Rule 1

    How angles in polygons behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How angles in polygons behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 3

    How angles in polygons behaves in the 3rd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
3 steps

How to work with angles in polygons

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing angles in polygons laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for angles in polygons in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: ×10\times 10 moves every digit one column left
3 rules

Key facts: Angles in polygons

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How angles in polygons behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How angles in polygons behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How angles in polygons behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
3 steps

How to work with angles in polygons

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
  1. Read the question and write down what is being asked for.
  2. Set out the working for angles in polygons in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}

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Examples

2 boxes
3 marks · worked

Worked example: angles in polygons

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 49=7\sqrt{49} = 7.
4 marks · worked

Practice question 9: a2+b2=c2a^2 + b^2 = c^2

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ×10\times 10 moves every digit one column left.

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Common questions

How many marks is angles in polygons usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Statistics OCR Foundation paper?
Yes — it sits in the Inheritance strand.