Central Angles of a Circle 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?

Here'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.

!clockfrace

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't equal the measures of the arc, then the angle of the hour-hand wouldn't equal the measure of the hour. That is, clocks simply would not work.