The bisector AD is drawn in an isosceles triangle ABC with base AC. Find ADC if C is 50 degrees.

1. ∠А = ∠С = 50 °, since, according to the properties of an isosceles triangle, the angles on the AC side are equal.

2. The bisector AD divides ∠A into two angles of equal magnitude:

∠ВАD = ∠САD = 25 °.

2. Based on the fact that the total value of the angles of the triangle ACD is 180 °, we calculate the value of ∠ADC:

∠АDС = 180 ° – ∠АСD – ∠САD = 180 ° – 50 ° – 25 = 105 °.

Answer: ∠ADC is equal to 105 °.