9th grade math question

Question

Triangle ABC is isosceles. Sides AB and BC are the legs. Point D lies somewhere on the base. Segment BD bisects the vertex angle. Angle A is 50 degrees. Segment DC is 4 feet long. What is the measure of Angle ABD? What is the length of segment AD?

Answer 1

Angle ABD = 65 degrees

AD = DC = 4 feet

all 3 angles in any triangle sum to 180

180 = 50 + 2x

2x = 130

x = 130/2 = 65 degrees = each of the other two angles including Angle ABD