My teacher said that the central angles of a circle are equal to the measure of the arc, but I don't understand on how this could possibly work.Can someone please explain how this is possible?

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My teacher said that the central angles of a circle are equal to the measure of the arc, but I don&#039;t understand on how this could possibly work.Can someone please explain how this is possible?

kejohananws · Accepted Answer

Here&#039;s an example that should hopefully help build intuition for this concept.Suppose you hear church bells tolling the hour, and so you check your watch to see what hour it is.The minute-hand (which will be pointing towards the 12) and hour-hand create a central-angle inside the cirlce of the clockface. The numbers 1 through 12 mark off measures of arc around the circle. If central angles didn&#039;t equal the measures of the arc, then the angle of the hour-hand wouldn&#039;t equal the measure of the hour. That is, clocks simply would not work.

Villaretq0 · Accepted Answer

This is why mathematicians like to measure angles in units of radians rather than degrees. Once around the circle is 360 degrees but only   2  π radians.Moreover, your teacher is talking about a circle whose radius is 1. I hope he or she remembered to mention that.

My teacher said that the central angles of a circle

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