2. 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.
a. Are the number of spokes and angles formed between the pairs of consecutive spokes in inverse proportion?
b. Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes
c. How many spokes would be needed, if the angle between a pair of consecutive spokes is 400?
Answers
Answer:
A table of the given information is as follows.
From the given table, we obtain
4\times90^{\circ}=\ 360^{\circ}=6\times60^{\circ}4×90
∘
= 360
∘
=6×60
∘
Thus, the number of spokes and the angle between a pair of consecutive spokes are inversely proportional to each other. Therefore,
4\times90^{\circ}=\ x_1\times84×90
∘
= x
1
×8
x_1=\frac{4\times90^{\circ}}{8}=45^{\circ}x
1
=
8
4×90
∘
=45
∘
Similarly, x_2=\frac{4\times90^{\circ}}{10}=36^{\circ}\ and\ x_3=\frac{4\times90^{\circ}}{12}=30^{\circ}x
2
=
10
4×90
∘
=36
∘
and x
3
=
12
4×90
∘
=30
∘
Thus, the following table is obtained.
(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 = \frac{360^{\circ}}{15}=24^{\circ}
15
360
∘
=24
∘
(iii) The number of spokes would be needed = \frac{360^{\circ}}{40^{\circ}}=\ 9
40
∘
360
∘
= 9
Hence, the number of spokes in such a wheel is 9.