### Video Transcript

Two straight lines, π΄π΅ and
πΆπ·, intersect at point πΈ. Fill in the blank. If the angles π΄πΈπ· and π΄πΈπΆ
are adjacent angles, where the union of rays πΈπΆ and πΈπ· equals the line
segment πΆπ·, then the measure of angle π΄πΈπΆ plus the measure of angle π΄πΈπ·
equals what. Fill in the blank. If the angles π΄πΈπΆ and πΆπΈπ΅
are adjacent angles, where the union of rays πΈπ΄ and πΈπ΅ equals the line
segment π΄π΅, then the measure of angle π΄πΈπΆ plus the measure of angle πΆπΈπ΅
equals what. True or False: We deduce from
the two parts above that the measure of angle π΄πΈπ· equals the measure of angle
πΆπΈπ΅.

Letβs begin this question by
drawing the two given lines, π΄π΅ and πΆπ·, which intersect at a point πΈ. Notice that we could have drawn
any different diagram of the lines π΄π΅ and πΆπ· that intersect at point πΈ, so
long as it shows that important line and intersection information. We would still be able to use
any such diagram to answer the questions.

So letβs use the first diagram
and look at the first part of this question. Here, we need to first identify
the angles π΄πΈπ· and π΄πΈπΆ. The second part of this
sentence, which tells us that the union of rays πΈπΆ and πΈπ· is the line
segment πΆπ·, is really stating the fact that these lines form one straight-line
segment. And what do we know about the
angles on a straight line? Well, the angle measures on a
straight line sum to 180 degrees. And so, the measure of angle
π΄πΈπ· plus the measure of angle π΄πΈπΆ is equal to 180 degrees. And thatβs the first missing
blank completed.

Letβs look at the second part
of the question. This time, weβre looking at the
angles π΄πΈπΆ and πΆπΈπ΅. Once again, weβre told that the
rays πΈπ΄ and πΈπ΅ form one straight-line segment, π΄π΅. And we know that the angle
measures on a straight line sum to 180 degrees. So these two angle measures of
π΄πΈπΆ and πΆπΈπ΅ will also sum to 180 degrees. So now we have answered the
second part of this question.

Letβs look at the final
part. In this part, we are
considering the angle measures of π΄πΈπ· and πΆπΈπ΅. To help us with this, weβll
consider what we discovered in parts one and two. In the first part, we
recognized that the measures of angles π΄πΈπΆ and π΄πΈπ· added to give 180
degrees. Letβs label the measure of
angle π΄πΈπ· as π₯ degrees and the measure of angle π΄πΈπΆ as π¦ degrees. In the second part of the
question, we identified another pair of angle measures that added to 180
degrees. And since π₯ degrees plus π¦
degrees equals 180 degrees, then we can say that the measure of angle πΆπΈπ΅ is
also π₯ degrees.

So, we can say that the
statement that the measure of angle π΄πΈπ· equals the measure of angle πΆπΈπ΅ is
true. And in fact, what we have here
is a proof that vertically opposite angles are equal. We could even have continued in
this example to demonstrate that the measure of angle π΄πΈπΆ equals the measure
of angle π·πΈπ΅. These vertically opposite
angles will both be π¦ degrees.