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From the information in the figure below, find πβ π΄πΈπΆ.

From the information in the figure below, find the measure of angle π΄πΈπΆ.

Angle π΄πΈπΆ is shown in the diagram. This can be split into the sum of two other angles, angle π΄πΈπΉ and angle πΆπΈπΉ. We can use our angle properties involving parallel lines to calculate these two values. The lines π΄π΅, πΈπΉ, and πΆπ· are parallel as indicated on the diagram. We know that alternate angles are congruent. These are sometimes referred to as βzeeβ or βzedβ angles. This means that angle π΅π΄πΈ is equal to angle π΄πΈπΉ. Theyβre both equal to 92 degrees.

Cointerior or supplementary angles sum to 180 degrees. These are often known as C angles. In this question, angle πΆπΈπΉ plus 131 degrees is equal to 180 degrees. This means that our missing angle π¦, angle πΆπΈπΉ, is equal to 49 degrees. We can therefore calculate the measure of angle π΄πΈπΆ by adding 92 degrees and 49 degrees. This is equal to 141 degrees.

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