Angle A of an isosceles trapezoid awsd with bases BC and AD is 54.

Angle A of an isosceles trapezoid awsd with bases BC and AD is 54. From point D a straight line is drawn that intersects line BC at point K, CD = DK. Find the angle CDK.

By the condition of the problem, the trapezoid is isosceles, the angles at the base are equal:
∠ A = ∠ D = 54 °.
∠ ADC = ∠ DCK = 54 ° (criss-crossing angles with parallel BC, AD and secant CD).
Consider an isosceles triangle CDK (CD = DK by condition), respectively, the angles at the base are:
∠ DCK = ∠ DKC = 54 °.
Find the angle D at the apex of an isosceles triangle:
∠ CDK = 180 ° – 2 * 54 ° = 72 °.
Answer: The degree measure of the CDK angle is 72 °.