Video Transcript
If the line segment 𝐴𝐵 is rotated
about 𝐴 with a 72-degree angle, which line segment represents its final
position? Option (A) the line segment 𝐴𝐶,
option (B) the line segment 𝐴𝐸, option (C) the line segment 𝐴𝐹, or option (D)
the line segment 𝐴𝐷.
We’re going to rotate the line
segment 𝐴𝐵 72 degrees about 𝐴. To do this, we firstly note that
the given polygon is a regular pentagon. We know that the sum of all the
angles around 𝐴 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, we’re rotating line segment
𝐴𝐵 in a counterclockwise direction about 𝐴 with a 72-degree angle. And because the measure of angle
𝐵𝐴𝐶 is 72 degrees, we see that the image of this line segment is the line segment
𝐴𝐶.
So, when we rotate 𝐴𝐵 about 𝐴
with a 72-degree angle, its final position is the line segment 𝐴𝐶.
