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°	…	…	…

(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°?

Answer 1

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° = x₁ × 8

Similarly, and

Thus, the following table is obtained.

Number of spokes	4	6	8	10	12
Angle between a pair of consecutive spokes	90°	60°	45°	36°	30°

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

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

4 × 90° = 15 × x

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

(iii) 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°

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