### Video Transcript

The speaker shown is an isosceles trapezoid. If the measure of angle πΉπ½π» equals 82 degrees, find the measure of angle πΉπΊπ».

Letβs highlight this trapezoidal shape and include the fact that the angle πΉπ½π» is 82 degrees. We can recall that a trapezoid or a trapezium is a quadrilateral with one pair of parallel sides. Further, weβre told that this speaker is an isosceles trapezoid. This means that the nonparallel sides in this quadrilateral are congruent. So here, the side πΉπ½ will be equal in length to the side πΊπ».

In order to find this unknown angle of πΉπΊπ», weβll need to use the properties of isosceles trapezoids. Because we have two legs that are congruent, then we can say that the lower base angles are congruent and the upper base angles are congruent. So angle πΉπ½π» will be the same as angle πΊπ»π½. And the upper base angles are congruent. So angle πΊπΉπ½ is congruent to angle πΉπΊπ». We could find the measure of angle πΉπΊπ» using a number of different methods. However, perhaps the quickest one is to use this final isosceles trapezoid property.

Any lower base angle is supplementary to any upper base angle. That means these will add to 180 degrees. We know this to be true because we have a pair of parallel sides. Therefore, the lower base angle and the upper base angle would add to 180 degrees. So we can set up an equation that this upper base angle that we wish to find out, angle πΉπΊπ», plus this lower base angle of πΉπ½π» must be equal to 180 degrees. We can plug in the information that angle πΉπ½π» is 82 degrees. And then subtracting 82 degrees from both sides of the equation would give us that the measure of angle πΉπΊπ» is 98 degrees.

We could, of course, also have answered this in a different way, remembering that the angles in a quadrilateral add to 360 degrees and given the lower base angles are congruent and the upper base angles are congruent. Defining our unknown upper base angles as the letter π₯, we could set up an alternative equation. Solving this, we would find that each of the upper base angles is 98 degrees, which also confirms our original answer that the measure of angle πΉπΊπ» is 98 degrees.