In triangle ABC, AB=AC and D is a point on line AC so that line BD bisects angle ABC. If AD=DC, what is the measure, in degrees, of angle A?
The answer is 60.
So first draw a diagram and label everything.
Then because of the angle bisector theorem, so AB/AD = CB/CD
You can write it as 2x/x = CB/x
From this you get CB = 2x.
Now you can tell the triangle is equilateral so the answer is 60.