### Video Transcript

Find the measure of angle π΅π΄πΈ.

In the diagram below, we have the large triangle π΅πΆπ· on the outside. And thereβs three different smaller triangles inside it. The angle that we need to find is this angle π΅π΄πΈ. We could find the measure of this angle if we knew the angle π·π΄πΆ and if we knew the angle πΆπ΄πΈ as we have a straight line. Or, if we looked at the smaller triangle π΅π΄πΈ, we could work out our missing angle if we knew this other angle π΅πΈπ΄. Now, it might be tempting to say that angle π΅πΈπ΄ looks like a 90-degree angle, but we donβt know this for sure, so we couldnβt use it in a calculation.

Instead, letβs look at the diagram and notice that we have some notation on the line sections to indicate that we have pairs of corresponding sides the same length. Letβs see if we can find if we have a pair of congruent triangles. We can remember that congruent triangles will be the same shape and size. The line π·π΄ on triangle π·π΄πΆ is marked as being the same length as line πΈπ΄ on triangle πΈπ΄πΆ. We have another pair of sides marked as the same length. Thatβs side π·πΆ and side πΈπΆ. Weβre not given any information about corresponding angles being the same, but we do actually have another side to consider: the line π΄πΆ is common to both triangles. And therefore, we can say that this is a corresponding congruent side in both triangles.

So now that weβve shown that we have three pairs of corresponding sides congruent, we can say that triangle π·π΄πΆ is congruent to triangle πΈπ΄πΆ by the SSS or side-side-side congruency criterion. So how does this help us with the original question to find the missing angle of π΅π΄πΈ? Well, we were given that this angle at πΆπ·π΄ is a right angle of 90 degrees, and so the corresponding angle at πΆπΈπ΄ would also be 90 degrees. We then use the fact that the angles on a straight line sum to 180 degrees, and our straight line πΆπ΅ means that the angle π΄πΈπ΅ will also be 90 degrees.

We can use our final angle fact to help us with this triangle π΅πΈπ΄. We can recall that the angles in a triangle add up to 180 degrees. To find our angle π΅π΄πΈ in this triangle π΅πΈπ΄, we calculate 180 degrees subtract 90 degrees subtract 46 degrees, which gives us the answer that the measure of angle π΅π΄πΈ is 44 degrees.