In the diagram below, triangle ABC is inscribed in the circle and AC = AB . The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD?
If AC = AB ....then triangle ABC is isosceles....with angles ABC and ACB being equal
And the measure of angle ABC = (180 - 42) / 2 = 69°
And since angle ABC is an inscribed angle, then minor arc AC will have twice the measure of angle ABC = 2 * 69 = 138°
And since ED is a tangent to the circle at C, then, by Euclid, angle ACD will have half the measure of minor arc AC = (1/2)138 = 69°