In an isosceles triangle ABC with a base AB, a bisector CD is drawn. Determine the angles ADC and ACD if the angle ACB = 80 °.

1. Consider the triangle ABC
angle ACB = 80 °
The sum of all the angles of a triangle will always be 180 °
The triangle is isosceles, so the angle ABC is equal to the angle BAC. We find their meaning:
(180 ° – 80 °) / 2 = 50 °
2. The bisector CD forms a new triangle ADC, consider it
The ACD angle is equal to half the ACB, since the bisector always divides the angle in half:
80 ° / 2 = 40 °
Find the angle ACD using the axiom that the sum of the angles in a triangle is 180
180 ° – 40 ° – 50 ° = 90 °
Answer: the ADC angle is 90 °, the ACD angle is 40 °.