In the trapezoid above, \(BC\) is parallel to \(AD,\) angle \(A\) is \(45\) degrees and the length of line segment

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In the trapezoid above, \(BC\) is parallel to \(AD,\) angle \(A\) is \(45\) degrees and the length of line segment \(CD\) is \(20.\) If the height of the trapezoid is \(10,\) then which of the following is the value of \(x+y?\)

A) 180

B) 255

C) 270

D) 285

E) 300

Answer: D

Source: EMPOWERgmat