Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms | Nagwa Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms | Nagwa

# Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms Mathematics • First Year of Preparatory School

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Find πβ πΉπΊπΈ.

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### Video Transcript

Find the measure of angle πΉπΊπΈ.

The diagram shows a parallelogram, where lines πΈπΉ and πΊπ» are parallel. The sides πΈπ» and πΉπΊ are also parallel. We can therefore use our angle properties involving parallel lines to find the measure of angle πΉπΊπΈ. We begin by recalling that alternate angles are congruent. These are often referred to as βzedβ or βzeeβ angles. In this question, angle π»πΊπΈ is equal to angle πΊπΈπΉ. They are both equal to 31 degrees.

πΈπΉπΊ 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 πΉπΊπΈ is equal to 43 degrees.

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