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

How many spokes would be needed, if the angle between a pair of consecutive spokes is ${40}^0$?.

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

$\begin{array}{cccccc}Numberofspokes& 4& 6& 8& 10& 12\\ Anglebetweenapairofconsecutivespokes& 90°& 60°& 45°& 36°& 30°\end{array}$

We need to find number of spokes if the angle is ${40}^o$

Let the number of spokes be $x$

Since number of spokes ang angle are in inverse proportion

So,

$x_1{y}_1=x_2{y}_2$

$4\times 90=x\times 40$

$x=\frac{4\times 90}{40}$

$x=9$

$\therefore$ Number of spokes are 9.