The bisector CD is drawn in an isosceles triangle ABC with base AC. Find the angles of triangle ADC if ABC = 80 degrees.

In an isosceles triangle, the angles at the base are equal.
Angle BAC = angle ACB and is equal to (180 ° -Angle ABC) / 2 = (180 ° -80 °) / 2 = 100 ° / 2 = 50 °. The DAC is 50 °.
Because CD is the bisector of ACB, then ACD is 1/2 of ACB and is 25 °.
In triangle ADC, the sum of the angles is 180 °.
Whence the ADC angle is 180 ° – (50 ° + 25 °) = 105 °.
Answer: angle DAC = 50 °, ACD = 25 ° and ADC = 105 °.