### Video Transcript

The figure shows a regular polygon. Where is the point π΅ moved to after a rotation through 240 degrees?

First, we note that the center of the polygon is point π. This is our center of rotation. We need to rotate π΅ 240 degrees about π. We recall that a rotation with a positive value will be in the counterclockwise direction. Since the polygon has nine sides, we know it is a nonagon.

We also note that the sum of the angles around π must be 360 degrees. And because the nonagon is regular, the nine central angles must be congruent. Then, each angle measure can be found by dividing 360 degrees by nine. Thus, each central angle has a measure of 40 degrees.

Since we want to rotate π΅ around π, letβs begin by sketching the circle with center π of radius ππ΅. We see that each rotation of 40 degrees moves us to the next point along the circle. We note that 240 degrees is equal to six times 40 degrees. So we can find the angle of measure 240 degrees on the diagram by rotating through six points in the counterclockwise direction. Finally, we see that point π΅ is moved to point π» following a 240-degree rotation about π.