In triangle ABC, angle C is 45 degrees, AD is the bisector of angle A, and ADB is 70 degrees.

In triangle ABC, angle C is 45 degrees, AD is the bisector of angle A, and ADB is 70 degrees. Find the degree measure of the angle B

The angles ADC and ADB are adjacent angles, the sum of which is 180, then the angle ADC = (180 – ADB) = (180 – 70) = 110.

In the triangle ACD, we determine the value of the angle CAD.

Angle CAD = (180 – ACD – ADC) = (180 – 45 – 110) = 25.

Since, by condition, AD is the bisector of the CAB angle, the CAB angle = 2 * CAD = 2 * 25 = 50.

Then in the triangle ABC we determine the value of the angle ABC.

Angle ABC = (180 – 45 – 50) = 85.

Answer: The angle B is 85.