### Video Transcript

In the figure below, the measure of
angle ๐ต๐ด๐ถ is equal to 30 degrees. If the ray from ๐ด through ๐ถ is an
angle bisector, what is the measure of angle ๐ต๐ด๐ท?

Letโs begin by identifying first
angle ๐ต๐ด๐ถ. Itโs the angle enclosed by the line
segments between ๐ต and ๐ด and ๐ด and ๐ถ. And so this angle here is 30
degrees. Now, weโre told that the line from
๐ด and passing through ๐ถ is an angle bisector. Now, a bisector cuts something in
half, so an angle bisector divides an angle exactly in half. And this therefore means that angle
๐ถ๐ด๐ท must be equal to angle ๐ต๐ด๐ถ. Itโs also 30 degrees.

Now weโre looking to find angle
๐ต๐ด๐ท. Thatโs this one on our diagram. We can say that itโs equal to the
measure of angle ๐ต๐ด๐ถ plus the measure of angle ๐ถ๐ด๐ท. Or alternatively since those angles
are equal, itโs two times the measure of angle ๐ต๐ด๐ถ. Thatโs two times 30, which is equal
to 60 degrees. The measure of angle ๐ต๐ด๐ท is 60
degrees. In general, we can say that an
angleโs bisector divides it into two equally sized adjacent angles.