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Angles in polygons

Angles in polygons for Functional Skills Business Studies: what it means, how to set the working out, and the questions it is asked in.
  • Functional Skills
  • Business Studies
  • Spec S4 · S8 · S18
  • 6 min read
  • 10 revision boxes

Introduction

2 boxes
3 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.
Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ×10\times 10 moves every digit one column left.
5 rows

The angles in polygons reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

6 boxes
3 steps

How to work with angles in polygons

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

Key facts: Angles in polygons

The examiner marks the working, so a correct answer with no method still drops marks.

  • 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.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

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

How to work with angles in polygons

Practise the routine version until it is automatic, then move to the multi-step questions.
  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: ≈160\approx 160.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Angles in polygons

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How angles in polygons behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • 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}
4 steps

How to work with angles in polygons

This idea appears again in the higher-mark questions, so it is worth over-learning.
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.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: 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: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How angles in polygons behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

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

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Examples

2 boxes
3 marks · worked

Worked example: angles in polygons

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: 49=7\sqrt{49} = 7.
4 marks · worked

Practice question 10: ×10\times 10 moves every digit one column left

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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.

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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 Functional Skills Business Studies paper?
Yes — it sits in the Inheritance strand.