### Video Transcript

Which of the following
inequalities is correct? (A) The measure of angle π΄π΅πΆ
is less than the measure of angle π΅π΄πΆ is less than the measure of angle
π΄πΆπ΅. Or (B) the measure of angle
π΄π΅πΆ is greater than that of angle π΅π΄πΆ which is greater than the measure of
angle π΄πΆπ΅. (C) The measure of angle π΅π΄πΆ
is greater than that of π΄π΅πΆ which is greater than that of π΄πΆπ΅. Or option (D), the measure of
angle π΅π΄πΆ is less than the measure of angle π΄π΅πΆ is less than that of
π΄πΆπ΅. Or finally, the measure of
angle π΄πΆπ΅ is less than the measure of angle π΄π΅πΆ which is less than the
measure of angle π΅π΄πΆ.

We note that each of the five
options involves the measures of the three angles π΄π΅πΆ, π΅π΄πΆ, and π΄πΆπ΅ and
that weβre given the measure of one of these. Thatβs angle π΄πΆπ΅, which is
29 degrees. And so to answer the question,
we need to find the measures of the two interior angles π΅π΄πΆ and π΄π΅πΆ.

We can find the measure of
angle π΅π΄πΆ by noting that the measures of the angles that make a straight line
sum to 180 degrees. And so we have 109 degrees plus
the measure of angle π΅π΄πΆ equals 180 degrees. Subtracting 109 degrees from
both sides gives us the measure of angle π΅π΄πΆ equals 71 degrees. Next, we can find the measure
of angle π΄π΅πΆ by recalling that the measure of the interior angles of a
triangle sum to 180 degrees. Thus, we have 71 degrees plus
the measure of angle π΄π΅πΆ plus 29 degrees equals 180 degrees.

Now, subtracting 71 and 29
degrees from both sides, we have the measure of angle π΄π΅πΆ equals 80
degrees. Since 80 is greater than 71,
which in turn is greater than 29, we see that the measure of angle π΄π΅πΆ is
greater than the measure of angle π΅π΄πΆ which is greater than the measure of
angle π΄πΆπ΅. And this corresponds to option
(B), so option (B) is correct.