Given: triangle ABC is isosceles, angle 1 is 120 degrees. Find angle 2 and angle 3.

Let angle 1 in an isosceles triangle ABC be angle B, whose value is 120 °.
Find the angles A and C in this triangle.
Since the sum of all angles in a triangle is 180 °, we write ABC for this triangle.
A + B + C = 180 °.
Since the angles at the base are equal in an isosceles triangle, angle 2 is equal to angle 3 or angle A is equal to angle C.
With this in mind, we write down the sum of all angles in a different way.
2A + B = 180 °.
Now we substitute in this equality the value of the angle B known from the problem statement and perform the necessary calculations.
2A + 120 ° = 180 °.
2A = 180 ° – 120 °.
2A = 60 °.
A = 60 °: 2.
A = 30 °.
By hypothesis, the angle A is equal to the angle C, so we write it down.
A = C = 30 °.
Answer: 30 ° is the value of angle 2 and angle 3.