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 spokes4681012Angle between a pair of consecutive spokes$$90^{\circ}$$$$60^{\circ}$$........How many spokes would be needed, if the angle between a pair of consecutive spokes is 40?

Solution

$$No.\quad of\quad spokes\quad =\quad n,\\ total\quad angle\quad in\quad the\quad wheel\quad =\quad 360\\ Angle\quad between\quad each\quad spoke\quad =\quad \frac { 360 }{ n } \\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 8)\quad =\quad \frac { 360 }{ 8 } \quad =\quad 45\\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 10)\quad =\quad \frac { 360 }{ 10 } \quad =\quad 36\\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 12)\quad =\quad \frac { 360 }{ 12 } \quad =\quad 30\\ Angle\quad between\quad each\quad spoke\quad =\quad 40\quad =\quad \frac { 360 }{ n } \quad \\ \quad \quad So\quad n\quad =\quad \frac { 360 }{ 40 } \quad =\quad 9$$Mathematics

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