### Video Transcript

If the line segment π΄π΅ is rotated
about π΄ with a 72-degree angle, which line segment represents its final
position? Option (A) the line segment π΄πΆ,
option (B) the line segment π΄πΈ, option (C) the line segment π΄πΉ, or option (D)
the line segment π΄π·.

Weβre going to rotate the line
segment π΄π΅ 72 degrees about π΄. To do this, we firstly note that
the given polygon is a regular pentagon. We know that the sum of all the
angles around π΄ must be 360 degrees. So, we can calculate the measure of
each angle at the center by calculating 360 divided by five. And we find that each angle at the
center has a measure of 72 degrees.

We also note that as we have been
asked to rotate by a 72-degree angle and 72 is positive, this rotation is
counterclockwise. So, weβre rotating line segment
π΄π΅ in a counterclockwise direction about π΄ with a 72-degree angle. And because the measure of angle
π΅π΄πΆ is 72 degrees, we see that the image of this line segment is the line segment
π΄πΆ.

So, when we rotate π΄π΅ about π΄
with a 72-degree angle, its final position is the line segment π΄πΆ.