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Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
Number of spokes 4 6 8 10 12
Angle between a pair of consecutive spokes $90^{0}$ $60^{0}$ ... ... ...
(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?

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Detailed Solution

Let the number of spokes be x and the angle between the pair of consecutive spokes be y.

So, $x \times y = k$ , where k is a constant.

$4 \times 90^{0} = 8 \times y_{3} .$

$\Rightarrow y_{3} = \frac{4 \times 90^{0}}{8} = 45^{0} .$

$4 \times 90^{0} = 10 \times y_{4} .$

$\Rightarrow y_{4} = \frac{4 \times 90^{0}}{10} = 36^{0} .$

$4 \times 90^{0} = 12 \times y_{5} .$

$\Rightarrow y_{5} = \frac{4 \times 90^{0}}{12} = 30^{0} .$

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