In a right-angled triangle ABC with a hypotenuse AB, the outer angle is 150 AC + AB = 12 cm, find the length of the hypotenuse.

1. According to the problem statement, the outer angle is 150º. The inner angle of the triangle at the vertex B can be calculated by subtracting it from the value of the extended angle:

180 – 150 = 30º.

2. The leg of the AC is opposite an angle of 30º.

3. Using the theorem that the leg opposite an angle of 30 degrees is equal to 1/2 of the hypotenuse of the triangle, we find the length of the leg AC:

AC = AB / 2.

3. AC = 12 – AB. We substitute here AC = AB / 2:

AB / 2 = 12 – AB;

1.5 AB = 12;

AB = 8 centimeters.

Answer: the length of the hypotenuse AB is 8 centimeters.