Answer :
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>