Question Video: Knowing that an Angle’s Bisector Divides it into 2 Equal Angles

Video Transcript

In the figure below, the measure of angle 𝐵𝐴𝐶 is equal to 30 degrees. If the ray from 𝐴 through 𝐶 is an angle bisector, what is the measure of angle 𝐵𝐴𝐷?

Let’s begin by identifying first angle 𝐵𝐴𝐶. It’s the angle enclosed by the line segments between 𝐵 and 𝐴 and 𝐴 and 𝐶. And so this angle here is 30 degrees. Now, we’re told that the line from 𝐴 and passing through 𝐶 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 𝐶𝐴𝐷 must be equal to angle 𝐵𝐴𝐶. It’s also 30 degrees.

Now we’re looking to find angle 𝐵𝐴𝐷. That’s this one on our diagram. We can say that it’s equal to the measure of angle 𝐵𝐴𝐶 plus the measure of angle 𝐶𝐴𝐷. Or alternatively since those angles are equal, it’s two times the measure of angle 𝐵𝐴𝐶. That’s two times 30, which is equal to 60 degrees. The measure of angle 𝐵𝐴𝐷 is 60 degrees. In general, we can say that an angle’s bisector divides it into two equally sized adjacent angles.