Video Transcript
In the figure below, the measure of
angle π΅π΄πΆ is equal to 30 degrees. If the ray from π΄ through πΆ is an
angle bisector, what is the measure of angle π΅π΄π·?
Letβs begin by identifying first
angle π΅π΄πΆ. Itβs the angle enclosed by the line
segments between π΅ and π΄ and π΄ and πΆ. And so this angle here is 30
degrees. Now, weβre told that the line from
π΄ and passing through πΆ 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
πΆπ΄π· must be equal to angle π΅π΄πΆ. Itβs also 30 degrees.
Now weβre looking to find angle
π΅π΄π·. Thatβs this one on our diagram. We can say that itβs equal to the
measure of angle π΅π΄πΆ plus the measure of angle πΆπ΄π·. Or alternatively since those angles
are equal, itβs two times the measure of angle π΅π΄πΆ. Thatβs two times 30, which is equal
to 60 degrees. The measure of angle π΅π΄π· is 60
degrees. In general, we can say that an
angleβs bisector divides it into two equally sized adjacent angles.