In trapezoid ABCD BC-less base. Point E is taken on segment AD so that BE || CD; angle ABE = 70 degrees

| June 24, 2021 | education

In trapezoid ABCD BC-less base. Point E is taken on segment AD so that BE || CD; angle ABE = 70 degrees, angle BEA = 50 degrees find the angles of the trapezoid.

Consider a triangle ABE, for which, on condition, two angles are known, then the angle BAD = 180 – 50 – 70 = 60.

Angle AED is deployed, then 1 head BED = 180 – AEB = 180 – 50 = 130.

Consider a quadrilateral EBSD, in which, according to the condition BE is parallel to CD and BC, parallel to ED, since ED belongs to the straight line AD, then BECD is a parallelogram, and its opposite angles are equal. BCD = BED = 130. Then the angle EDC = EBC = CDA = (360 – 130 – 130) / 2 = 50. Angle ABC = ABE + EBC = 70 + 50 = 120.

Answer: The angles of the trapezoid are BAD = 60, ABC = 120, BCD = 130, CDA = 50.



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