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:

(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

Here the number of spokes are increasing and the angle between a pair of consecutive spokes is decreasing. So, it is a inverse proportion and angle at the centre of a circle is 360 degree. 

When the number of spokes is 8, then angle between a pair of consecutive spokes = 360/8=45 degree 

When the number of spokes is 10, then angle between a pair of consecutive spokes= 360/10=36 degree 

When the number of spokes is 12, then angle between a pair of consecutive spokes= 360/12=30 degree.

(i) Yes, the number of spokes and the angles formed between a pair of consecutive spokes is in inverse proportion. 

(ii) When the number of spokes is 15, then angle between a pair of consecutive spokes = 360/15=24 degree. 

(iii) The number of spokes would be needed = 360/40=9 degree