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

In the figure below, π‘šβˆ π΅π΄πΆ = 30Β°. If the ray 𝐴𝐢 is an angle bisector, what is π‘šβˆ π΅π΄π·?


Video Transcript

In the figure below, the measure of angle 𝐡𝐴𝐢 is equal to 30 degrees. If the ray from 𝐴 through 𝐢 is an angle bisector, what is the measure of angle 𝐡𝐴𝐷?

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

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

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