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Hi. This is my question:

An art student wants to make a string collage by connecting six equally spaced points on the circumference of a circle to its center with string. What would be the radian measure of the angle between two adjacent pieces of string, in simplest form?

This is a math b regents practice tests question, and I have no idea how to solve it. Please help me! Thank You!

  • Math -

    Um... I think its 60* ... I think if not, sorry


  • Math -

    Since all 6 points on the circumference of the circle are equally spaced, the string running from each outer point to, and around the center point, and back to the next outer point forms 6 equilateral triangles. The 6 angles formed by the radial strings from the center to the outer points sum to 360º making the central angle of each triangle 60º. By definition therefore, the remaining two angles within each triangle must total 120º making the two outer angles of each triangle 60º each.

    The angles between adjacent outer string sides of the hexagon are therefore 120º apart.

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