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Rehman is making a wheel using spokes. He wants to fix equal spokes n 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 angle 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∘?
Rehman is making a wheel using spokes. He wants to fix equal spokes n such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table

Solution:

Let the number of spokes be x and the angle between the pair of consecutive spokes be y

Two numbers x and y are said to be in inverse proportion when an increase in one quantity decreases the other quantity and vice versa.

xy = k or x = (1/y) k

where k is a constant.

x₁y₁ = x₃y₃

4 × 90° = 8 × y₃

y₃ = 4 × 90°/8 = 45°

x₁y₁ = x₄y₄

4 × 90° = 10 × y₄

y₄ = 4 × 90°/10 = 36°

x₁y₁ = x₅y₅

4 × 90° = 12 × y₅

y₅ = 4 × 90°/12 = 30°

Thus, the table is shown below:

Number of spokes           4 6 8         10       12      
Angle between spokes 90° 40° 30° 36° 45°

(i) We can observe from the data given in the table: when the number of spokes was 4, the angle between the pair of consecutive spokes was 90º, and when the number of spokes was 6, the angle between the pair of consecutive spokes was 60°. Thus we see that, if the number of spoke increases, then the angle between the spoke decreases. Hence they are in inverse variation.

(ii) Let the number of spokes be x and the angle between the pair of consecutive spokes be y

x₁y₁ = x₃y₃

4 × 90° = 15 ×y₂

y₂ = 4 × 90°/15 = 24°

The angle between the pair of consecutive spokes on a wheel with 15 spokes is 24°.

(iii) Let the number of spokes be x and the angle between the pair of consecutive spokes be y

x₁y₁ = x₂y₂

4 × 90° = x₂ × 40º

x₂ = 4 × 90°/40 = 9

If the angle between a pair of consecutive spokes is 40°, then the spokes on the wheel are 9.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 13

Video Solution:

Rehman is making a wheel using spokes. He wants to fix equal spokes n such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table

NCERT Solutions Class 8 Maths Chapter 13 Exercise 13.2 Question 3

Summary:

Rehman is making a wheel using spokes. He wants to fix equal spokes n such a way that the angles between any pair of consecutive spokes are equal. We have completed the table. (i) If the number of spoke increases, then the angle between the spoke decreases. Hence it is inversely proportional (ii) The angle between the pair of consecutive spokes on a wheel with 15 spokes is 24° (iii) the angle between a pair of consecutive spokes is 40°, then the spokes on the wheel are 9

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