Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
An isosceles trapezoid has two congruent legs and one pair of parallel sides. The base angles are congruent to one another, and by same side interior angles, the upper angles are supplementary to the respective base angles, meaning that they are both 180° - (the measure of the base angle).
So, if given the measure of one of the upper angles, you know that its base angle is supplementary to it, so subtract its value from 180° to find the measure of the base angle. Then, recall that in an isosceles trapezoid, the base angles are congruent. The other upper angle is supplementary to its base angle, so it is thus congruent to the upper angle. Thus, from just one angle in an isosceles trapezoid, it is possible to find the measures of the other angles.
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. So let’s go over and take a look at what we know about isosceles trapezoids.
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. 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.
So let's go back to our problem. 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. Well I know that these two must be supplementary because they are on the same side of this transversal BC. So if B is 110 C must be what? 180 minus 110 which 70 degrees. So I’m going to write in here that C must be 70 degrees.
Now you just have to remember that your base angles are congruent to each other. So I’m going to write that D must be 70 degrees and on that A must be 110 degrees. So A we said was 110 and D we said was 70 degrees. The key thing here was remembering that same side interior angles are supplementary and that base angles in an isosceles trapezoid are always congruent.