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
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