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? (ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. (iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?

Here the number of spokes are increasing and the angle between a pair of consecutive
spokes is decreasing. So, it is a inverse proportion and angle at the centre of a circle is 360°.
When the number of spokes is 8,
then angle between a pair of consecutive spokes = 360°/8 =45°
When the number of spokes is 10,
then angle between a pair of consecutive spokes = 360°/10 =36°
When the number of spokes is 12,
then angle between a pair of consecutive spokes = 360°/12 =30°

No. of spokes 4 6 8 10 12
Angle between a pair of consecutive spokes 90° 60° 45° 36° 30°

(i) Yes, the number of spokes and the angles formed between a pair of
consecutive spokes is in inverse proportion.
(ii) When the number of spokes is 15, then angle between a pair of consecutive
spokes = 360°/15 = 24°
(iii) The number of spokes would be needed = 360°/40° = 9°

Class 8 Maths Chapter 11 Exercise 13.2 Solution in Video

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