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Angle BAE is part of a regular 18-sided polygon - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

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Angle BAE is part of a regular 18-sided polygon. Angle CAD is part of a regular 10-sided polygon. The dashed line through A is a line of symmetry of both polygons. ... show full transcript

Worked Solution & Example Answer:Angle BAE is part of a regular 18-sided polygon - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Step 1

Work out the internal angle of a regular 18-sided polygon

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Answer

To find the internal angle of a regular polygon, we use the formula:

extInternalangle=(n−2)×180n ext{Internal angle} = \frac{(n-2) \times 180}{n}

For an 18-sided polygon (n = 18):

extInternalangle=(18−2)×18018=16×18018=160∘ ext{Internal angle} = \frac{(18-2) \times 180}{18} = \frac{16 \times 180}{18} = 160^{\circ}

Step 2

Work out the internal angle of a regular 10-sided polygon

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Answer

Using the same formula for a 10-sided polygon (n = 10):

extInternalangle=(10−2)×18010=8×18010=144∘ ext{Internal angle} = \frac{(10-2) \times 180}{10} = \frac{8 \times 180}{10} = 144^{\circ}

Step 3

Determine angle BAC

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Answer

Since the dashed line through A is a line of symmetry for both polygons, angle BAC divides the sum of angles BAE (from the 18-sided polygon) and CAD (from the 10-sided polygon) equally.

Thus, angle BAC can be calculated as:

Angle BAC=(160∘+144∘)2=304∘2=152∘\text{Angle BAC} = \frac{(160^{\circ} + 144^{\circ})}{2} = \frac{304^{\circ}}{2} = 152^{\circ}

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