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

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

Answer 1

Since a wheel is in shape of a circle, central angle of wheel $={360}^o$

$\therefore$ Angle between spokes $=\frac{Centralangle}{Numberofspokes}$

If number of spokes $=8$

Angle between spokes $=\frac{{360}^o}{8}$

$={45}^o$

If number of spokes $=10$

Angle between spokes $=\frac{{360}^o}{10}$

$={36}^o$

If number of spokes $=12$

Angle between spokes $=\frac{{360}^o}{12}$

$={30}^o$

So, our table become

$\begin{array}{cccccc}Numberofspokes& 4& 6& 8& 10& 12\\ Anglebetweenapairofconsecutivespokes& 90°& 60°& 45°& 36°& 45°\end{array}$

As we increase the number of spokes,

The angle between consecutive spokes decreases.

$\therefore$ They are in inverse proportion.