Pretend you are explaining to another student the procedure for converting the measure of an angle from degrees to radians. She asks, "Why?

Radians are universal. No matter what system you use, radians are always the same.

Degrees are man-made. You could easily use 100 degrees = 1 circle.

If you do a good job explaining what radians are and why they are better then she shouldn't ask why. If she does then explain the conversation factor, divide by 360 to find how many revolutions to times by 2pi to convert that into radians so that is the same as multiplying pi/180

There are π radians in 180 degrees. So if you set it up as a proportion:

π/180 = x/360

Then solving for x, you end up taking the 360 and multiplying it by π/180 to get your answer. So no matter what angle is used in degrees, multiplying by π/180 will always convert it to radians.