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	${90}^{\circ }$	${60}^{\circ }$	...	...	..

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

Answer 1

No. of spokes $=n$

Total angle in the wheel $=360$

Angle between each spoke $=\frac{360}{n}$

Angle between each spoke $(n=8)=\frac{360}{8}=45$

Angle between each spoke $(n=10)=\frac{360}{10}=36$

Angle between each spoke $(n=8)=\frac{360}{12}=30$

Yes, they are inversely proportional.

$4=>{90}^{\circ }$

$6=>{60}^{\circ }$

$8=>{45}^{\circ }$

$10=>{36}^{\circ }$

$12=>{30}^{\circ }$