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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 Tabl - Mathematics

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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° 60° ... ... ...

1) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

2) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.

3) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?

#### Solution

A table of the given information is as follows.

 Number of spokes 4 6 8 10 12 Angle between a pair of consecutive spokes 90° 60° x1 x2 x3

From the given table, we obtain

4 × 90° = 360° = 6 × 60°

Thus, the number of spokes and the angle between a pair of consecutive spokes are inversely proportional to each other. Therefore,

4 × 90° = x× 8

x_1 = (4 xx 90^@)/8 = 45^@

Similary, x_2 = (4 xx 90^@)/10 =  36^@  and x_3 = (4 xx90^@)/12 = 30^@

Thus, the following table is obtained.

 Number of spokes 4 6 8 10 12 Angle between a pair of consecutive spokes 90° 60° 40° 36° 30°

1) Yes, the number of spokes and the angles formed between the pairs of consecutive spokes are in inverse proportion.

2) Let the angle between a pair of consecutive spokes on a wheel with 15 spokes be x. Therefore,

4 × 90° = 15 × x

x =  (4 xx 90^@)/15 = 24^@

Hence, the angle between a pair of consecutive spokes of a wheel, which has 15 spokes in it, is 24°.

3) Let the number of spokes in a wheel, which has 40º angles between a pair of consecutive spokes, be y

Therefore,

4 × 90° = y × 40°

y = (4 xx 90)/40 =  9

Hence, the number of spokes in such a wheel is 9.

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