Q3. 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.

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

Number of spokes

    4     6    8    10  12

Angle between a pair of consecutive 

  90^{\circ}   60^{\circ}   ....     ....  ....

 

 

 

Answers (1)

(i) Calculating the angle formed when using a different number of spokes:

The angle formed when using 8, 10, and 12 number of spokes a1,a2, and a3 respectively.

Hence, we have 

For 8 number of spokes:

\frac{360^{\circ}}{8} = 45^{\circ}

For 10 number of spokes:

\frac{360^{\circ}}{10} = 36^{\circ}

For 12 number of spokes:

\frac{360^{\circ}}{12} = 30^{\circ}

Number of spokes (x) 4 6 8 10 12
Angle between a pair of consecutive spokes (y) 90° 60° 45° 36°

30°

Calculating xy:

4\times90^{\circ} = 6\times60^{\circ} = 8\times45^{\circ}=10\times36^{\circ}=12\times30^{\circ}=360^{\circ}

Hence we say that the number of spokes (x) and the angle formed (y) between them are inverse proportion to each other.

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