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When ABCD is drawn to scale, would the lines AD and BC be parallel or not? You must justify your answer without using a scale drawing.

A = 2x degrees
B = 90 degrees
C = x degrees
D = 3x degrees

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sqdancefan

Answer:

  yes, they are parallel

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°, so ...

  2x + 90 + x + 3x = 360

  6x = 270 . . . . . subtract 90

  2x = 90 . . . . . . divide by 3

Then angles A and B are both 90°, meaning sides AD and BC are parallel.

_____

The same-side interior angles at transversal AB between lines AD and BC are supplementary, so the crossed lines (AD and BC) are parallel.

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