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Work out the size of the exterior angle of a regular 12-sided polygon - OCR - GCSE Maths - Question 5 - 2020 - Paper 6

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Work out the size of the exterior angle of a regular 12-sided polygon. (a) Use your answer to part (a) to write down the size of the interior angle of a regular 1... show full transcript

Worked Solution & Example Answer:Work out the size of the exterior angle of a regular 12-sided polygon - OCR - GCSE Maths - Question 5 - 2020 - Paper 6

Step 1

Work out the size of the exterior angle of a regular 12-sided polygon.

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Answer

To calculate the exterior angle of a regular polygon, we can use the formula:

ext{Exterior Angle} = rac{360^ ext{o}}{n}

where n is the number of sides. For a 12-sided polygon (dodecagon), we find:

ext{Exterior Angle} = rac{360^ ext{o}}{12} = 30^ ext{o}

Thus, the exterior angle of a regular 12-sided polygon is 30exto30^ ext{o}.

Step 2

Use your answer to part (a) to write down the size of the interior angle of a regular 12-sided polygon.

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Answer

The interior angle can be found by using the relationship between exterior and interior angles:

extInteriorAngle=180exto−extExteriorAngle ext{Interior Angle} = 180^ ext{o} - ext{Exterior Angle}

From part (a), we calculated the exterior angle to be 30exto30^ ext{o}, so:

extInteriorAngle=180exto−30exto=150exto ext{Interior Angle} = 180^ ext{o} - 30^ ext{o} = 150^ ext{o}

Therefore, the size of the interior angle of a regular 12-sided polygon is 150exto150^ ext{o}.

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