In a right-angled triangle ABC with a hypotenuse AC, the outer angle at the apex A

In a right-angled triangle ABC with a hypotenuse AC, the outer angle at the apex A is 120 degrees, AB = 5 cm. Find the length of the hypotenuse of the triangle.

Outside apex angle A and BAC add up to 180 degrees. Hence it follows that
BAC angle = 180-120 = 60 degrees.
Angle ACB = 180-90-60 = 30 (according to the theorem on the sum of the angles of a triangle)

According to the properties of a right-angled triangle, opposite an angle of 30 degrees lies a leg equal to half of the hypotenuse. Hence AC = 2 * AB = 2 * 5 cm = 10 cm.