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Question 336573: How does my daughter write a general rule or formula for finding the number of angles that can be named by a given number of rays with the same endpoint? Can you explain why the rule works? All rays lie on one side of a straight line. I've looked and looked at this and know it must be simple but I can't figure out how to say/do it. Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I believe the formula you are looking for is that the number of angles that can be named with a given number of rays is equal to the number of rays minus 1.
Think of a fan that has 7 spines.
each spine is a ray.
The part where the fan opens from is the common point.
The spaces between the spines form the angles.
the number of angles is 1 less than the number of spines.
Number the spines 1 through 7
angle 1 is between spine 1 and 2
angle 2 is between spine 2 and 3
angle 3 is between spine 3 and 4
angle 4 is between spine 4 and 5
angle 5 is between spine 5 and 6
angle 6 is between spine 6 and 7
that's 6 angles with 7 spines.
If the fan only had 3 spines, then you would have 2 angles and 3 spines.
angle 1 between spine 1 and 2
angle 2 between spine 2 and 3.
the number of angles will always be one less than the number of spines.
since the spines form the function of rays, then the formula is that the number of angles will always be one less than the number of rays.
If your daughter is in elementary school, then I believe this answer will suffice.
I can't think they would want to make it any more complex than that.
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