Question Video: Properties of Parallel Lines Mathematics • 8th Grade

From the information in the figure below, find ๐‘šโˆ ๐ด๐ธ๐ถ.

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Video Transcript

From the information in the figure below, find the measure of angle ๐ด๐ธ๐ถ.

Angle ๐ด๐ธ๐ถ is shown in the diagram. This can be split into the sum of two other angles, angle ๐ด๐ธ๐น and angle ๐ถ๐ธ๐น. We can use our angle properties involving parallel lines to calculate these two values. The lines ๐ด๐ต, ๐ธ๐น, and ๐ถ๐ท are parallel as indicated on the diagram. We know that alternate angles are congruent. These are sometimes referred to as โ€œzeeโ€ or โ€œzedโ€ angles. This means that angle ๐ต๐ด๐ธ is equal to angle ๐ด๐ธ๐น. Theyโ€™re both equal to 92 degrees.

Cointerior or supplementary angles sum to 180 degrees. These are often known as C angles. In this question, angle ๐ถ๐ธ๐น plus 131 degrees is equal to 180 degrees. This means that our missing angle ๐‘ฆ, angle ๐ถ๐ธ๐น, is equal to 49 degrees. We can therefore calculate the measure of angle ๐ด๐ธ๐ถ by adding 92 degrees and 49 degrees. This is equal to 141 degrees.

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