# Video: Finding the Measure of an Internal Angle in Congruent Triangles

Given that π΅πΆ = π΄π·, π΄πΆ = π΄πΈ, and πβ πΆπ΄π΅ = 68Β°, find πβ πΈπ΄π·.

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### Video Transcript

Given that π΅πΆ equals π΄π·, π΄πΆ equals π΄πΈ, and the measure of angle πΆπ΄π΅ equals 68 degrees, find the measure of angle πΈπ΄π·.

In this question, we can see that we have two triangles. And weβre asked to find a measure of angle πΈπ΄π·. So letβs compare our triangles and see if we have enough information to allow us to find the missing angle. Starting with the line π΅πΆ in triangle π΄πΆπ΅, weβre told that itβs equal to the line π΄π· in triangle πΈπ΄π·. Weβre also told that thereβs another pair of equivalent sides. Side π΄πΆ in triangle π΄πΆπ΅ is equivalent to side π΄πΈ in triangle πΈπ΄π·. Weβre not given any equivalences for the third side in each of the triangles. But letβs have a look at the angles.

We can see that the measure of angle πΆπ΅π΄ is a 90-degree angle. And we can also see another 90-degree angle. Thatβs the angle πΈπ·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΄πΆπ΅ and πΈπ΄π· are congruent using the SSA congruency criterion; thatβs side, side, angle. Notice that it wouldnβt be the SAS criterion, since the angle isnβt the included angle between the two sides.

Letβs 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 πΈπ΄π·, must be equal to the angle π΄πΆπ΅ in triangle π΄πΆπ΅. Weβre not given an angle measurement for this angle. But letβs see if we can work it out. Weβre going to use the fact that the angles in a triangle add up to 180 degrees. So the measure of angle π΄πΆπ΅ 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΄πΆπ΅ is 22 degrees. Then the equivalent angle πΈπ΄π· is also 22 degrees. So our final answer is the measure of angle πΈπ΄π· is 22 degrees.