# 3.Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consective spokes are equal. Help him by completing the following table. (i) Are the number of spokes and the angle 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 $$40^o$$?

From the given table we have, $$4\times90^o=6\times60^o$$

$$\Rightarrow 360^o=360^o$$

Thus, we can say that quantities are inversely peoportional

Let the blacks be as a,b and c

So we have, $$4\times90^o=8\times a$$

$$\Rightarrow a=\frac{4\times 90^o}{8}=45^o$$

Similarly, $$4\times90^o=10\times b$$

$$\Rightarrow b=\frac{4\times 90^o}{10}=36^o$$

And, $$4\times90^o=12\times c$$

$$\Rightarrow c=\frac{4\times 90^o}{12}=30^o$$

Hence, we have the table as:

(i) Yes, they are in inverse proportion

(ii) If the number of spokes is 15, then

$$4 \times 90^o = 15 \times x$$

$$x = \frac { 4\times 90 }{ 15 } = 24^o$$

(iii) If the angle between two consecutive spokes is $$40^o$$, then

$$4 \times 90^0 = y \times 40^o$$

$$y = \frac { 4\times 90 }{ 40 } = 9 spokes.$$

Thus the required number of spokes = 9.<\br>