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°	60°	...	...	...

1. Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
2. Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
3. How many spokes would be needed if the angle between a pair of consecutive spokes is 40°?

Answer 1

• Number of sticks = 8
  The angle between each pair of consecutive spokes = `360/8`
  = 45°
• Number of sticks = 10
  The angle between each pair of consecutive spokes = `360/10`
  = 36°
• Number of sticks = 12 The angle between each pair of consecutive spokes is `360/12`
  = 30°

Number of spokes	4	6	8	10	12
Angle between a pair of consecutive spokes	90°	60°	45°	36°	30°

According to the question:

1. Yes, the number of spokes and the angle between any pair of consecutive spokes are inversely proportional.
2. Number of sticks = 15
   Angle between each pair of consecutive spokes = `360/15`
   = 24°
3. Given angle between each pair of consecutive spokes = 40°
   number of sticks required will be = `360/40`
   = 9
   Hence, number of sticks required = 9