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RS and ST are 2 sides of a regular 12-sided polygon - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 2

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Question 12

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RS and ST are 2 sides of a regular 12-sided polygon. RT is a diagonal of the polygon. Work out the size of angle STR. You must show your working.

Worked Solution & Example Answer:RS and ST are 2 sides of a regular 12-sided polygon - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 2

Step 1

Find the interior angle of the polygon

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Answer

The formula to find the interior angle of a regular polygon is:

extInteriorAngle=(n−2)×180n ext{Interior Angle} = \frac{(n-2) \times 180}{n} where n is the number of sides. In this case, n = 12.

Calculating:

Interior Angle=(12−2)×18012=10×18012=180012=150°\text{Interior Angle} = \frac{(12-2) \times 180}{12} = \frac{10 \times 180}{12} = \frac{1800}{12} = 150°

Step 2

Calculate angle STR

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Answer

Since RT is a diagonal that connects vertices, angle STR can be calculated as follows:

Angle STR=180°−Interior Angle2=180°−150°2=180°−75°=105°\text{Angle STR} = 180° - \frac{\text{Interior Angle}}{2} = 180° - \frac{150°}{2} = 180° - 75° = 105°

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