In trapezoid ABCD, it is known that AB = CD, AC = AD and angle ABC = 107 degrees. Find the CAD corner.

According to the properties of a trapezoid, the sum of the angles at its lateral sides is 180.

Then the angle BAD + ABC = 180.

Angle BAD = 180 – 107 = 73.

Since, by condition, AB = CD, the trapezoid ABCD is isosceles, and therefore, its angles at the bases are equal to each other.

Angle BAD = CDA = 73, angle BCD = ABC = 107.

By condition, AC = AD, then triangle ACD is isosceles and its angle ADC = ACD = 73.

Then the angle CAD = 180 – ADC – ACD = 180 – 73 – 73 = 34.

Answer: Angle CAD = 34.