From the diagram, angle C is a right angle because it is formed by a perpendicular line. It means that
Angle BCD + 46 = 90
angle BCD = 90 - 45 = 44 degrees
The opposite angles in a parallelogram are equal while the adjacent angles are supplementary. Angle ABC and angle BCD are supplementary and the sum of supplementary angles is 180 degrees. Therefore,
The known acute angle of the triangle is 46 degrees, so the unknown acute angle of that triangle is 90-46 = 44 degrees. In other words, the two acute angles of any right triangle must add to 90, so 46+44 = 90.
The 44 degree angle is adjacent to angle ADC, and it adds to angle ADC to form 180 degrees.
If x is the measure of angle ADC, then
44+(angleADC) = 180
44+x = 180
x = 180-44
x = 136
angle ADC = 136 degrees
For any parallelogram, the opposite angles are always congruent. Therefore, angle ABC is equal to angle ADC = 136, making ABC = 136 as well.
