In triangle ABC, angle C is straight, B is the outer angle at the vertex A = 150 degrees. Find the sides BC and AB if BC + AB = 24CM.

When building the drawing, I took the outer corner not as B, but as D. Since we have a triangle ABC, it is inconvenient to write the same letters.
If we build a drawing, we get a right-angled triangle ABC with an external angle BAD at apex A and a hypotenuse AB.
Angle CAB = 180-150 = 30 ° (angles CAB and BAD are adjacent).
We were given the sum of the leg and the hypotenuse. (24cm)
We found that the angle CAB = 30 °.
Received a leg, which lies opposite an angle of 30 ° (leg CB). By the property of a right-angled triangle, it is equal to half the hypotenuse. That is, the hypotenuse AB is twice the leg CB.
Take the leg for x, then the hypotenuse is 2x. (2 times more).
Let’s make an equation.
2x + x = 24
Let’s solve:
3x = 24.
x = 24: 3
x = 8
We got that the leg CB = 8cm. Hypotenuse = 2 × 8 = 16.
Answer: AB = 16, CB = 8.