### Video Transcript

Given that the measure of angle
π΄πΈπΆ equals 36 degrees and the measure of angle π΅π΄π· equals four π₯ minus eight
degrees, determine the value of π₯.

We are given, firstly, that the
measure of angle π΄πΈπΆ is 36 degrees. The measure of angle π΅π΄π· is four
π₯ minus eight degrees. We donβt have any theorems that
tell us immediately how these two angles are related. So letβs observe that we are given
a set of parallel line segments. The line segment π΄π΅ is parallel
to the line segment πΆπ·. And so we can say that this angle
of π΄π·πΆ must be alternate to angle π΅π΄π·. So they will have equal angle
measures of four π₯ minus eight degrees.

Now, we can use the property that
inscribed angles subtended by the same arc are equal. We should observe that this arc
π΄πΆ subtends two angles, angle π΄π·πΆ and angle π΄πΈπΆ, meaning that these two
angle measures will be the same. And so we can set up an equation
that four π₯ minus eight degrees is equal to 36 degrees. Since the brackets on the left-hand
side are simply there just to indicate that this is a measure in angles, then we can
drop the brackets and the degrees from both sides of the equation. We can then add eight to both
sides, giving us four π₯ is equal to 44. Dividing both sides of the
equation, we have the answer that π₯ is equal to 11.