In a right-angled triangle, one of the outer angles is 120 degrees, find the smaller leg of the triangle if its hypotenuse is 4 cm.

1. Subtracting the external angle equal to 120º from the value of the expanded angle, we calculate the value of one of the acute angles of the triangle:

180º – 120º = 60º.

2. Considering that the sum of the angles of the triangle is 180º, we calculate another acute angle:

180º – 60º – 90º = 30º.

3. Since the length of the leg located opposite the angle of 30º is 1/2 of the hypotenuse, we calculate the length of this leg;

4: 2 = 2 cm.

4. Applying the Pythagorean theorem, we calculate the length of the other leg:

√16 – 4 = √12 = √4 x 3 = 2√3 cm.

Answer: the length of the smaller leg is 2 cm.