Question 30714
LET ABCD BE THE QUADRILATERAL...WE ARE GIVEN
ANGLE A = ANGLE B = X SAY.....AND
ANGLE C = ANGLE D = Y SAY......
SUM OF 4 ANGLES IN A QUADRILATERAL =360...SO
X+Y+X+Y = 360
2(X+Y)=360
X+Y=180
NOW SINCE AB AND CD ARE 2 LINES AND BC IS A TRANSVERSAL,WE HAVE 2 INTERIOR ANGLES 
ON THE SAME SIDE OF TRANSVERSAL..NAMELY ANGLE B =X  AND ANGLE C =Y....THEIR SUM 
X+Y = 180.....HENCE THEY SHOULD BE PARALLEL.
SO AB IS PARALLEL TO CD...HENCE ABCD IS A TRAPEZOID.