  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 spokes4681012Angle 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 $$40$$? Solution

$$k = 4\times 90 = 360$$ degreesAngle for $$8$$ spoke $$= \dfrac {360}{8} = 45$$ degreesAngle for $$10$$ spoke $$= \dfrac {360}{10} = 36$$ degreesAngle 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 $$= \dfrac {360}{40} = 9$$ spokesMathematicsNCERTStandard VIII

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