In the diagram below, triangle $ABC$ is inscribed in the circle and $AC = AB$. The measure of angle $BAC$ is $30$ degrees and segment $ED$ is tangent to the circle at point $C$. What is the measure of angle $ACD$?

Since AB = AC and BAC = 30

Then angle ACB = (180 -30) / 2 = 75

And since BAC = 30.....then minor arc BC = 60...so angle BCE = (1/2)(60) = 30

So angle ACD =180 - BCE - ACB = 180 - 75 - 30 = 75°