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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 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?

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Solution

## k=4×90=360 degreesAngle for 8 spoke =3608=45 degreesAngle for 10 spoke =36010=36 degreesAngle for 12 spoke =36012=30 degrees(i) As with increasing no. of spokes the angle is decreasing so they are in inverse proportion(ii) Required angle =36015=24 degrees(iii) No. of spokes needed =36040=9 spokes

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