# Question Video: Finding the Measure of an Angle Using the Congruence of Triangles Mathematics • 8th Grade

Find πβ π΅π΄πΈ.

02:48

### Video Transcript

Find the measure of angle π΅π΄πΈ.

In the diagram below, we have the large triangle π΅πΆπ· on the outside. And thereβs three different smaller triangles inside it. The angle that we need to find is this angle π΅π΄πΈ. We could find the measure of this angle if we knew the angle π·π΄πΆ and if we knew the angle πΆπ΄πΈ as we have a straight line. Or, if we looked at the smaller triangle π΅π΄πΈ, we could work out our missing angle if we knew this other angle π΅πΈπ΄. Now, it might be tempting to say that angle π΅πΈπ΄ looks like a 90-degree angle, but we donβt know this for sure, so we couldnβt use it in a calculation.

Instead, letβs 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. Letβs 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΄πΆ is marked as being the same length as line πΈπ΄ on triangle πΈπ΄πΆ. We have another pair of sides marked as the same length. Thatβs side π·πΆ and side πΈπΆ. Weβre not given any information about corresponding angles being the same, but we do actually have another side to consider: the line π΄πΆ is common to both triangles. And therefore, we can say that this is a corresponding congruent side in both triangles.

So now that weβve shown that we have three pairs of corresponding sides congruent, we can say that triangle π·π΄πΆ is congruent to triangle πΈπ΄πΆ 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΄πΈ? Well, we were given that this angle at πΆπ·π΄ is a right angle of 90 degrees, and so the corresponding angle at πΆπΈπ΄ 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 πΆπ΅ means that the angle π΄πΈπ΅ will also be 90 degrees.

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