### Video Transcript

Find the measure of angle
πΉπΊπΈ.

The diagram shows a parallelogram,
where lines πΈπΉ and πΊπ» are parallel. The sides πΈπ» and πΉπΊ are also
parallel. We can therefore use our angle
properties involving parallel lines to find the measure of angle πΉπΊπΈ. We begin by recalling that
alternate angles are congruent. These are often referred to as
βzedβ or βzeeβ angles. In this question, angle π»πΊπΈ is
equal to angle πΊπΈπΉ. They are both equal to 31
degrees.

πΈπΉπΊ is a triangle. And we know that angles in a
triangle sum to 180 degrees. This means that π₯ plus 31 plus 106
is equal to 180. Simplifying this gives us π₯ plus
137 is equal to 180. Finally, subtracting 137 from both
sides gives us π₯ equals 43. We can therefore conclude that the
measure of angle πΉπΊπΈ is equal to 43 degrees.