In a right-angled triangle ABC, angle C is straight, angle B is 45 degrees, AC = 6 Find BC.

By the theorem on the sum of the angles of a triangle, we find the angle A:
angle A + angle B + angle C = 180 degrees;
angle A + 45 + 90 = 180;
angle A = 180 – 135;
angle A = 45 degrees.
Since the angle A = 45 degrees, the angle B = 45 degrees, then the angle A = angle B. Then the angle ABC is an isosceles triangle, AC and BC are the sides, and angles A and B are the angles at the base. Since the sides of an isosceles triangle are equal, AC = BC = 6 conventional units.
Answer: BC = 6 conventional units.