# 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 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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