# Find CAD in an isosceles trapezoid ABCD, angle ABC = 127.

Since this is an isosceles trapezoid, side AB = CD, AC = AD. Angle CDA = Angle BAD, Angle ABC = Angle BCD.

Since it is a trapezoid, the angle ABC + BAD = 180 degrees.

So the angle BAD = 180 – 127 = 53 degrees = angle CDA.

Since AC = AD, the angle CDA = ACD = 53 degrees.

The angles in a triangle add up to 180 degrees:

CDA + ACD + CAD = 180 = 53 + 53 + CAD.

This means that the angle СAD = 180 – 106 = 80 – 6 = 74 degrees.

Answer: 74.

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