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.

(i) Are the number of spokes and the angles formed between the pairs ofconsecutive spokes in inverse proportion?

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

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

(i) The table of the required information is as follows:

Number of spokes | 4 | 6 | 8 | 10 | 12 |

Angle between a pair of consecutive spokes | 90° | 60° | X1 | X2 | X3 |

4 × 90° = 6 × 60° = 360°

Therefore the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion.

(ii) 4 × 90° = 15 × angle

Angle = 24°

the angle between a pair of consecutive spokes on a wheel with 15spokes is 24°

(iii) 4 × 90° = 40° × spokes

→spokes = 9

9 spokes would be needed, if the angle between a pair of consecutive spokes is 40°

10