 # NCERT Solutions Class 8 Mathematics Solutions for Exercise 13.2 in Chapter 13 - Direct and Inverse Proportions

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

degree?

Solution:

Here the number of spokes is increasing and the angle between a pair of consecutive spokes is

decreasing. So, it is an inverse proportion and the angle at the center of a circle is 360 degrees.

When the number of spokes is 8, then the angle between a pair of consecutive spokes = 360/8 = 45 degree

When the number of spokes is 10, then the angle between a pair of consecutive spokes= 360/10= 36 degree.

When the number of spokes is 12, then the angle between a pair of consecutive spokes= 360/12 = 30

degree. (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 the angle between a pair of consecutive spokes= 360/15= 24

degree.

(iii) The number of spokes would be needed = 360/40 = 9

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