in a quad ABCD of the given fig AB parallel to DC  and AB = DC if angle B 75 degree find the measure of other angle

As AB and DC are parallel and equal, the quadrilateral becomes a parallelogram 

As we know by the properties of the parallelogram :
=> opposite angles are equal

Therefore angle D = angle B = 75 degree
As we also know that the sum of all the angles of a quadrilateral = 360 degree
Therefore angle(A+B+C+D) = 360 degree
this implies that angle (A+C) = (360-75-75) degree
this implies that angle (A+C) = 210 degree

As we showed before that opposite angles are equal,
We get angle A = angle C = (210/2) degree each
Therefore we now get angle A and C both = 105 degree

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As AB IS PARALLEL TO DC.
B=D =vertically opposite angle
B=D=75degree
B+A=180 =SUM OF PARALLEL SIDES OF A PARALLELOGRAM IS 180degree
75+A=180
A=180-75
A=105 degree
A=C=VERTICALLY OPPOSITE ANGLE
C=105 degree
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oh
 
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