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Angles in polygons

Angles in polygons for ESOL Economics: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Economics
  • Spec A9 · A14
  • 6 min read
  • 7 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.
The examiner marks the working, so a correct answer with no method still drops marks.
3 rows

The angles in polygons reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
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
49=7\sqrt{49} = 7
Row 3 column 4

Learning

3 boxes
5 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.
  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.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Angles in polygons

Practise the routine version until it is automatic, then move to the multi-step questions.
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.

  • Rule 1

    How angles in polygons behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • 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.
    49=7\sqrt{49} = 7
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: ×10\times 10 moves every digit one column left.
  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: 49=7\sqrt{49} = 7.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}

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Examples

2 boxes
4 marks · worked

Worked example: angles in polygons

Read the units in the question before you start; a converted unit is the most common slip.
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.
4 marks · worked

Practice question 7: x2+5x+6=0x^2 + 5x + 6 = 0

Read the units in the question before you start; a converted unit is the most common slip.

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Topics
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Marking and solutions
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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 ESOL Economics paper?
Yes — it sits in the Inheritance strand.