In the triangle ABC AC = BC, the outer angle at the apex of the base is 140 °, find the angle C.

If in a triangle AC = BC, then it is isosceles, therefore the angles at the base AB will be equal: angle A = angle B.
To see the outer angle at the top of the base, you need to lengthen the base AB in one of the sides, for example, towards angle B, and mark, say, with point E. Then the angle CBE is 140 °. Angle B will then be equal to 180 ° -140 ° = 40 ° (subtract the angle CBE from the unfolded angle ABE), as well as angle A. In a triangle, there are only 180 ° for all 3 internal angles, therefore, we must subtract angles A and B to get angle C.
180 ° -40 ° -40 ° = 100 ° – angle С