Since the diagonal BD is perpendicular to the side AB, the triangle ABD is rectangular.
Then SinBAD = BD / AD = 7/12.
Angle BAD = arcsin (7/12) ≈ arcsin (0.583) ≈ 35.7.
The sum of the adjacent angles of the parallelogram is 180, then the angle ABC = 180 – BAD = 180 – 35.7 = 144.3.
In a parallelogram, the opposite angles are equal, then the angle BCD = ABD = 35.7, the angle ADC = ABC = 144.3.
Answer: The angles of the parallelogram are 35.7 and 144.3.
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