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Find πβ πΉπΊπΈ.

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.

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