In triangle ABC, angle A is 35 degrees. Angle B is 80 degrees, bisected by angle B. Find angles ADB, BDC, and ACB.

Determine the value of the angle ACB.

Angle ACB = (180 – ABC – BAC) = (180 – 80 – 35) = 65.

Since BD is the bisector of the angle ABC, then the angle CBD = ABD = ABC / 2 = 80/2 = 40.

In triangle ABD we define the value of the angle ADB.

Angle ADB = (180 – ABD – BAD) = (180 – 40 – 35) = 105.

The angles ADB and CDB are adjacent, the sum of which is 180, then the angle BDC = (180 – ADB) = (180 – 105) = 75.

Answer: The ADB angle is 105, the BDC angle is 75, the ACB angle is 65.