What is the smallest number of rays starting at one point should be drawn so that all the angles

What is the smallest number of rays starting at one point should be drawn so that all the angles formed by adjacent rays are sharp?

Four beams with 90º angles between them will occupy 360º.

If we reduce one of the corners, making it sharp, that is, less than 90º, then one of the angles will surely become more than 90º,

That is, it will become dull. Therefore, the number of rays must be more than four.

Five rays, evenly spaced around the circumference, with angles between them 360º / 5 = 72º, satisfy the given task.



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