In trapezoid ABCD AB = CD, AC = AD and angle ABC = 117. Find angle CAD.

For a trapezoid, the sum of the angles at the sides is 180.

Angle ABC + BAD = 180. Then angle BAD = 180 – 117 = 63.

Since, by condition, AB = CD, the trapezoid is isosceles, and therefore the angle ADC = BAD = 63.

Consider a triangle ACD, which, by condition, has a segment AC = AD, then the triangle is isosceles and the angle ACD = ADC = 63.

Then the value of the angle CAD = 180 – 63 – 63 = 54.

Answer: Angle CAD = 54.