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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 spokes
4
6
8
10
12
Angle between a pair of consecutive spokes
$$90^{\circ}$$
$$60^{\circ}$$
...
...
..
Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.


Solution

$$
No.\quad of\quad spokes\quad =\quad n,\\ total\quad angle\quad in\quad the\quad wheel\quad =\quad 360\\ Angle\quad between\quad each\quad spoke\quad =\quad \frac { 360 }{ n } \\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 8)\quad =\quad \frac { 360 }{ 8 } \quad =\quad 45\\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 10)\quad =\quad \frac { 360 }{ 10 } \quad =\quad 36\\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 12)\quad =\quad \frac { 360 }{ 12 } \quad =\quad 30\\ Angle\quad between\quad each\quad spoke\quad (n\quad =\quad 15)\quad =\quad \frac { 360 }{ 15 } \quad =\quad 24
$$

Mathematics

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