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Here is a regular hexagon and a regular pentagon - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 1

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Question 7

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Here is a regular hexagon and a regular pentagon. Work out the size of the angle marked x. You must show all your working.

Worked Solution & Example Answer:Here is a regular hexagon and a regular pentagon - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 1

Step 1

Finding the interior angle of the pentagon

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Answer

The formula for the interior angle of a regular polygon is given by:

extInteriorAngle=(n−2)×180∘n ext{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}

Where n is the number of sides. For a pentagon (n = 5):

Interior Angle=(5−2)×180∘5=3×180∘5=108∘\text{Interior Angle} = \frac{(5-2) \times 180^\circ}{5} = \frac{3 \times 180^\circ}{5} = 108^\circ

Step 2

Finding the interior angle of the hexagon

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Answer

For a hexagon (n = 6):

Interior Angle=(6−2)×180∘6=4×180∘6=120∘\text{Interior Angle} = \frac{(6-2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = 120^\circ

Step 3

Calculating angle x

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Answer

The angle x can be calculated by subtracting the interior angles of the pentagon and the hexagon from 360 degrees (since they are on a straight line):

x=360∘−(120∘+108∘)x = 360^\circ - (120^\circ + 108^\circ)

x=360∘−228∘=132∘x = 360^\circ - 228^\circ = 132^\circ

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