In trapezoid ABCD, it is known that the sides are equal, AD and BC are the bases of the trapezoid, the angle CAD = 46

In trapezoid ABCD, it is known that the sides are equal, AD and BC are the bases of the trapezoid, the angle CAD = 46 and the angle CAB = 28. find the ACD angle.

Since the sides of the trapezoid ABCD are equal, this trapezoid is isosceles, therefore the angles at its bases are equal, that is: angle A = angle D, angle B = angle C.
1. Find angle A.
angle A = angle CAD + angle CAB;
angle A = 46 degrees + 28 degrees;
angle A = 74 degrees.
Since angle A = angle D, then angle D = 74 degrees.
2. Consider a CAD triangle: CAD angle = 46 degrees (by condition), D = 74 degrees.
From the theorem on the sum of the angles of a triangle, it is known that the sum of all the angles of any triangle is 180 degrees, therefore:
CAD angle + D angle + ACD angle = 180 degrees;
46 degrees + 74 degrees + ACD angle = 180 degrees;
ACD angle = 180 degrees – 46 degrees – 74 degrees;
angle ACD = 60 degrees.
Answer: ACD angle = 60 degrees.