# A straight line is drawn through the vertex C of the trapezoid ABCD, which is parallel to the side of AB

August 23, 2021 | education

| **A straight line is drawn through the vertex C of the trapezoid ABCD, which is parallel to the side of AB and and intersects the larger base AD at point E, find the corners of the trapezoid if the angle D = 35, DCE = 65.**

By the property of a trapezoid, the sum of the angles at the sides of the trapezoid is 180.

Angle ADC + BCD = 180.

ВСD = 180 – АDC = 180 – 65 = 115.

Then the angle BCE = BСD – DCE = 115 – 35 = 80.

The ABCE quadrilateral is a parallelogram since its opposite sides are parallel. In a parallelogram, opposite angles are equal, then the angle BAE = BAD = BCE = 80.

Then the angle ABC = 180 – BAD = 180 – 80 = 100.

Answer: The angles of the trapezoid are 80, 100, 115, 65.

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