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Question

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
$$90^{\circ}$$
$$60^{\circ}$$
...
...
..
Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

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Solution

No. of spokes $$= n$$
Total angle in the wheel $$= 360$$
Angle between each spoke $$= \cfrac { 360 }{ n }$$
Angle between each spoke $$(n = 8) = \cfrac { 360 }{ 8 }  = 45$$
Angle between each spoke $$(n = 10) = \cfrac { 360 }{ 10 }  = 36$$
Angle between each spoke $$(n = 8) = \cfrac { 360 }{ 12 }  = 30$$
Yes, they are inversely proportional.
$$4 => 90^{\circ}$$
$$6=>60^{\circ}$$
$$8=>45^{\circ}$$
$$10=>36^{\circ}$$
$$12=>30^{\circ}$$

Mathematics

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