### Video Transcript

Given that π΅πΆ equals π΄π·, π΄πΆ equals π΄πΈ, and the measure of angle πΆπ΄π΅ equals 68 degrees, find the measure of angle πΈπ΄π·.

In this question, we can see that we have two triangles. And weβre asked to find a measure of angle πΈπ΄π·. So letβs compare our triangles and see if we have enough information to allow us to find the missing angle. Starting with the line π΅πΆ in triangle π΄πΆπ΅, weβre told that itβs equal to the line π΄π· in triangle πΈπ΄π·. Weβre also told that thereβs another pair of equivalent sides. Side π΄πΆ in triangle π΄πΆπ΅ is equivalent to side π΄πΈ in triangle πΈπ΄π·. Weβre not given any equivalences for the third side in each of the triangles. But letβs have a look at the angles.

We can see that the measure of angle πΆπ΅π΄ is a 90-degree angle. And we can also see another 90-degree angle. Thatβs the angle πΈπ·π΄. And since both of these angles are 90 degrees, then we have two equivalent angles. So looking at three pieces of information on the triangles, we have information regarding two sides and another piece of information about one of the angles. We can conclude that our two triangles π΄πΆπ΅ and πΈπ΄π· are congruent using the SSA congruency criterion; thatβs side, side, angle. Notice that it wouldnβt be the SAS criterion, since the angle isnβt the included angle between the two sides.

Letβs see if using the fact that these triangles are congruent will help us find our missing angle. So looking at our triangles, then the angle that we want to find out, that is, angle πΈπ΄π·, must be equal to the angle π΄πΆπ΅ in triangle π΄πΆπ΅. Weβre not given an angle measurement for this angle. But letβs see if we can work it out. Weβre going to use the fact that the angles in a triangle add up to 180 degrees. So the measure of angle π΄πΆπ΅ is equal to 180 degrees subtract 68 degrees subtract 90 degrees. So this simplifies to 22 degrees. So now, we know that the measure of angle π΄πΆπ΅ is 22 degrees. Then the equivalent angle πΈπ΄π· is also 22 degrees. So our final answer is the measure of angle πΈπ΄π· is 22 degrees.