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Trapezoid Properties - Problem 2
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 base angles, you know that the other base angle is congruent to it in an isosceles trapezoid, so it has the same measure. Then, the upper angles are supplementary to the base angles, so subtract the value of the base angle from 180° to find the measure of the upper angles.
Using what know about isosceles trapezoids, which are identified by looking at congruent bases when we have another pair of bases that are parallel, we can use the fact that same side interior angles are always going to be supplementary.
So x here plus 60 must be 180 which means x is 120 degrees. Y we know is going to be congruent to 60 degrees. So I’m going to say that y is 60 degrees.
Again the key thing here is remembering that your base angles are going to be congruent to each other and that these two same side interior angles will be supplementary.
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