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5 (a) 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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5 (a) Work out the size of the exterior angle of a regular 12-sided polygon. (b) Use your answer to part (a) to write down the size of the interior angle of a regu... show full transcript

Worked Solution & Example Answer:5 (a) 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 find the exterior angle of a regular polygon, we can use the formula:

extExteriorAngle=360n ext{Exterior Angle} = \frac{360}{n}

Where ( n ) is the number of sides.

For a 12-sided polygon:

extExteriorAngle=36012=30exto ext{Exterior Angle} = \frac{360}{12} = 30^ ext{o}

Thus, the size of the exterior angle is ( 30^ 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 of a polygon can be found using the relation:

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

From part (a), we have the exterior angle as ( 30^ ext{o} ):

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 ( 150^ ext{o} ).

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