Video Transcript
Find the measure of the arc that represents one-sixth of the circumference of a circle.
We recall first that an arc is a portion of the circumference of a circle. The measure of an arc is the measure of its central angle, that is, the measure of the angle formed between the two radii connecting the endpoints of the arc to the center of the circle. In our diagram here, we’ve labeled the measure of the central angle and, hence, the measure of the arc highlighted in orange as 𝜃 degrees.
Now, we’re asked to find the measure of the arc that represents one-sixth of the circumference of a circle. This also means that the measure of the central angle will be one-sixth of the measure of a full turn. We know of course that a full turn is 360 degrees. So one-sixth of this is 60 degrees. The measure of the arc that represents one-sixth of the circumference of a circle is 60 degrees.
