AB perpendicular to DE, angle ABC = 180 °, angle CDE = 150 ° .prove that BC is perpendicular to CD

univerkov | February 2, 2021 | education

Let’s construct a perpendicular ВD between the segments AB and DE.

Then the angle СВD = (ABC – AВD) = (120 – 90) = 30.

Angle ВDС = (СDE – ВDE) = (150 – 90) = 60.

The sum of the inner angles of the triangle is 180, then in the ВСD triangle, the ВСD angle = (180 – СВD – ВDС) = (180 – 30 – 60) = 90.

Consequently, the BC is perpendicular to the СD, as required.

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