In isosceles triangle ABC Bisector AD is drawn with base AC. find the ADC angle if the angle is C = 50 degrees.

Since in any isosceles triangle the angles at the base are equal, and the base of this isosceles triangle is the segment AC, then ∠BAC = ∠BCA.

According to the condition of the problem, the BCA angle is 50 °, therefore, the BCA angle is also 50 °

Consider triangle ADC.

Since in any triangle the sum of the angles is always 180 °, the following relationship takes place:

180 ° = ∠ADC + ∠BAC + ∠BCA = ∠ADC + 50 + 50 = ∠ADC + 100,

whence it follows that ∠ADC = 180 – 100 = 80 °.

Answer: ∠ADC = 80 °.