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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 (in degrees): 90, 60, ..., ..., ... (i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

Solution:

k=4×90=360 degrees
Angle for 8 spokes = 360/8 = 45 degrees
Angle for 10 spokes = 360/10 = 36 degrees
Angle for 12 spokes = 360/12 = 30 degrees
(i) As with increasing number of spokes the angle is decreasing so they are in inverse proportion
(ii) Required angle = 360/15 = 24 degrees
(iii) Number of spokes needed = 360/40 = 9 spokes