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? 
+4623 Isn't this an angle formed by a tangent and chord. If so, we have angle B and C as 180-42=138 divided by 2 equals 69. Since arc AC has the twice angle measure of angle B, we get 138. Learn this, pretty useful. Thus, angle ACD is 69 degrees.
+4623 We can start off by using the finding angle B. We have \(\frac{180-42}{2}=\frac{138}{2}=69^\circ\) . Now, by the tangent formula, the arc AC is twice angle B, so \(69*2=138^\circ\) . Now, finally the chord and tangent, we have \(\frac{1}{2}*138^\circ=\boxed{69^\circ}.\)
+129935 Since AB = AC the angles opposite these sides are equal
So m ABC = [ 180 - m BAC] /2 = [ 180 - 42 ] / 2 = 138/2 = 69°
And since ABC is an inscribed angle, then it intercepts an arc that is twice its measure
So minor arc AC = 138°
And a chord meeting a tangent forms an angle = 1/2 the arc intercepted by the chord
So chord AC intercepts minor arc AC....so....
m angle ACD = 138 / 2 = 69°
