Triangle ABC is isosceles with base AC. Define angle 2 if angle 1 is 56 degrees.

In an isosceles triangle, the angles at the base are equal, that is, the angle BAC = the angle of the BCA. It is also known that the sum of the angles of a triangle is 180 °. Therefore: 1) If the known angle 1 is the angle BAC, then the angle BCA = angle BAC = 56 °, and the angle ABC = 180 ° – (angle BAC + angle BCA) = 180 ° – (56 + 56) = 68 °. 2) If the known angle 1 is the angle ABC, then the angle BAC = angle BCA = (180-56) / 2 = 62 °.