![]() The key thing here was remembering that same side interior angles are supplementary and that base angles in an isosceles trapezoid are always congruent. The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary. He also proves that the perpendicular to the base of an isosceles triangle bisects it. So A we said was 110 and D we said was 70 degrees. Sal proves that the base angles in isosceles triangles are congruent, and conversely, that triangles with congruent base angles are isosceles. So I’m going to write that D must be 70 degrees and on that A must be 110 degrees. Now you just have to remember that your base angles are congruent to each other. So I’m going to write in here that C must be 70 degrees. So if B is 110 C must be what? 180 minus 110 which 70 degrees. ![]() Well I know that these two must be supplementary because they are on the same side of this transversal BC. If I look at the only thing that we know about this trapezoid that’s angle B which is 110 degrees, I could start of by finding angle C. We also know that the same side interior angles here, so I’m looking at these triangles right here, are going to be supplementary that’s the definition of same side interior. ![]() ![]() Well we see that the base angles, so if I’m looking at two base angles, they are going to be congruent to each other. So let’s go over and take a look at what we know about isosceles trapezoids. In this problem we have an isosceles trapezoid which means we have two legs that are congruent when we have a pair of parallel sides. ![]()
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