In triangle ABC, angle A = 10 degrees, AC = BC. Find corner C.

If in a triangle ABC AB = BC, then the triangle is isosceles.
If AC = BC, then the base angles are A and B.
In an isosceles triangle, the angles at the base are equal. Means:
angle A = angle B = 10 °.
The sum of all the angles of a triangle is 180 °.
Thus:
angle C = 180 – (angle A + angle B);
angle C = 180 – (10 + 10);
angle C = 180 – 20 = 160.
Answer: angle C is 160 °.