The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other?

The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other? Class 6

Question 1.

The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other? What is the largest acute angle formed between two spokes? Class 6

Solution:

Angle between two spokes = [latex]\frac{360^{\circ}}{24}[/latex] = 15°

The largest acute angle that can be formed between two spokes is 5 × 15° = 75°.

It is because after the next spoke, the angle will be 6 × 15° = 90°, which is a right angle.

Question 2.

Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple my measure, you will get an acute angle again. If you quadruple (four times) my measure, you will get an acute angle yet again! But if you multiply my measure by 5, you will get an obtuse angle measure. What are the possibilities for my measure? Class 6

Solution:

We know that 18° × 5 = 90°, which is a right angle.

So, the required angle must be greater than 18°.

Thus angle can be 19°, 20°, 21°, 22°, 23°, ...

But 23° × 4 = 92°, which is an obtuse angle.

Hence, 23° cannot be that angle.

Thus, possible values of integral values of angles satisfying the above puzzle are 19°, 20°, 21°, and 22°.