### Video Transcript

Given that the measure of angle πΈπ΄π· equals 80 degrees and line segment π΄π· is
parallel to line segment π΅πΆ, what is the measure of angle πΆπ΅πΈ?

We can begin this problem by adding the measure of angle πΈπ΄π·, which is 80 degrees,
to the diagram and note that we are told that line segments π΄π· and π΅πΆ are
parallel. We need to find the measure of angle πΆπ΅πΈ. Since we have two parallel lines and the transversal π΄π΅, then the measure of angle
πΆπ΅πΈ is simple to calculate. Because these are alternate angles, then the measure of angle πΆπ΅πΈ is equal to the
measure of angle πΈπ΄π·, and they will both be 80 degrees.

Although we have found the answer, itβs worth taking a closer look at whatβs going on
in this particular diagram. And it involves similar triangles. We can recall that similar triangles have corresponding angles congruent and
corresponding sides in proportion. But it might be easy to think that we donβt have enough information to prove that
these two triangles are similar. However, letβs consider the angles. If we can prove that all the corresponding pairs of angles in these triangles are
congruent, then the triangles are similar. And we can prove this even without knowing that angle πΈπ΄π· is 80 degrees.

We do already know that because of the parallel lines and the transversal, angles
πΆπ΅πΈ and π·π΄πΈ will be congruent because these are alternate angles. Angles π΅πΆπΈ and π΄π·πΈ are also alternate angles, and so these are congruent. And finally, angles πΆπΈπ΅ and π·πΈπ΄ are congruent because they are opposite
angles. This is sufficient to prove that triangles πΆπ΅πΈ and π·π΄πΈ are similar. And therefore, if we want to find the measure of angle πΆπ΅πΈ, we know that it will
be the same as angle π·π΄πΈ. And we were given that angle πΈπ΄π· is 80 degrees.

Notice that it doesnβt matter if we give this angle as angle π·π΄πΈ or πΈπ΄π·, so
long as the letter π΄ is in the middle to represent that the vertex of the angle is
at point π΄. And because the corresponding angle πΆπ΅πΈ is congruent, it also has a measure of 80
degrees, which confirms the original answer.