### Video Transcript

Find the value of π₯.

We see from the figure that the
lines π΄πΆ and π΄π΅ are transversals that intersect parallel lines π·πΈ and
π΅πΆ. And we know that the two pairs
of corresponding angles created by this intersection are equal. Thatβs angles π·πΈπ΄ and π΅πΆπ΄
and angles πΈπ·π΄ and πΆπ΅π΄. This being the case, we can say
the triangles π΄π΅πΆ and π΄π·πΈ are similar triangles since they each have the
common angle π΅π΄πΆ and their other two angles are also equal.

Now recall that when two
triangles are similar, the ratios of the length of their corresponding sides are
equal. In particular, π΄π· is to π΄π΅
as π·πΈ is to π΅πΆ. In other words, π΄π· over π΄π΅
is equal to π·πΈ over π΅πΆ. Now, we know that π΄π· is equal
to 10 units. π΄π΅ is equal to 10 plus 11
units, thatβs π΄π· plus π·π΅. π·πΈ is equal to 10 units, and
π΅πΆ is π₯. And so we have 10 over 10 plus
11 is equal to 10 over π₯. That is, 10 over 21 is equal to
10 over π₯.

Now, solving for π₯, we
multiply through by 21π₯ and divide both sides by 10, and we have π₯ equal to
21. Hence, using the given diagram,
we find that π₯ is equal to 21 units.