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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 spokes4681012
Angle between a pair of consecutive spokes (in degrees)9060 .........

(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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Solution

$$k = 4\times 90 = 360$$ degrees

Angle for $$8$$ spoke $$= \dfrac {360}{8} = 45$$ degrees

Angle for $$10$$ spoke $$= \dfrac {360}{10} = 36$$ degrees

Angle for $$12$$ spoke $$= \dfrac {360}{12} = 30$$ degrees

(i) As with increasing no. of spokes the angle is decreasing so they are in inverse proportion
(ii) Required angle $$= \dfrac {360}{15} = 24$$ degrees
(iii) No. of spokes needed $$= \dfrac {360}{40} = 9$$ spokes

Mathematics
NCERT
Standard VIII

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