In quadrilateral ABCD , AB = CD and BC = AD . If \angle CBD = 30 degrees and \angle BAD = 80 degrees, what is the value of \angle ADC ?
(C) 2008 GMAT Club - m24#8
* 30 degrees
* 50 degrees
* 70 degrees
* 100 degrees
* 120 degrees
Because AB = CD and BC = AD , ABCD is a parallelogram. \angle ADC = \angle BDA + \angle BDC = \angle CBD + \angle ABD = \angle CBD + (180 - \angle BAD - \angle BDA) = 30 + (180 - 80 - 30) = 100
Can we conclusively say that a quadrilateral whose opposite sides are equal will always be a parallelogram? Don't we need to know if the opposite sides are parallel as well to determine if it is a parallelogram? I can't think of any other scenario than parallelogram but want to confirm.
IMO, if opposite sides of a quadrilateral are equal we can safely assume that it is a parallelogram.
-------Analyze why option A in SC wrong-------