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.

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Triangle ABC is an equilateral triangle. Therefore, angle A = 60 degrees.