### Video Transcript

Triangle ๐ด ๐ต prime ๐ถ prime is
the image of triangle ๐ด๐ต๐ถ by a counterclockwise rotation of ๐ฅ degrees about
๐ด. Find ๐ฅ.

So, in this question, weโre given
that thereโs a rotation. Triangle ๐ด๐ต๐ถ is rotated, and
weโre told that the direction is counterclockwise, to give us triangle ๐ด ๐ต prime
๐ถ prime. The angle of rotation is ๐ฅ
degrees, and we need to work out what ๐ฅ is.

The center of rotation of this
rotation is at vertex ๐ด, which explains why thereโs no new image of ๐ด of ๐ด
prime. In order to work out the angle of
rotation between an object and its image, we can calculate the angle between any
vertex and the image of that vertex. Letโs begin with vertex ๐ต. We know that itโs rotated
counterclockwise to the image ๐ต prime. If we joined each vertex, ๐ต and ๐ต
prime, with a line to the center of rotation, then to find the angle of rotation, we
just need to find the angle between these two lines.

So, ๐ฅ, the angle of rotation, is
equal to 37 degrees plus 69 degrees, which means that ๐ฅ is equal to 106. We can check our answer by finding
the angle between ๐ถ and ๐ถ prime. To find the angle here, once again
weโll be adding 69 degrees and 37 degrees, which gives us an answer of 106.