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A regular polygon has n sides - OCR - GCSE Maths - Question 11 - 2018 - Paper 6

Question 11

A regular polygon has n sides. The polygon's interior angle is 5 times the size of its exterior angle. Find n.

Worked Solution & Example Answer:A regular polygon has n sides - OCR - GCSE Maths - Question 11 - 2018 - Paper 6

Step 1

Find the relationship between the interior and exterior angles

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Answer

Let the exterior angle be denoted as x. Therefore, the interior angle can be expressed as 5x.

We know that the sum of the interior and exterior angle is: $ext{Interior Angle} + ext{Exterior Angle} = 180$ This gives us: $5x + x = 180$

Step 2

Solve for x

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Answer

Combining the terms gives: $6x = 180$ Dividing both sides by 6 results in: $x = 30$ Thus, the exterior angle is 30 degrees.

Step 3

Calculate the number of sides n

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Answer

The formula to find the number of sides n of a regular polygon is given by: $n = \frac{360}{\text{Exterior Angle}}$ Substituting the value of the exterior angle, we have: $n = \frac{360}{30} = 12$

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