In a right-angled triangle ABC with a hypotenuse AB, the outer angle at apex B is 120 °.

In a right-angled triangle ABC with a hypotenuse AB, the outer angle at apex B is 120 °. BC + AB = 15 cm. Find the length of the hypotenuse of the triangle.

The sum of the outer angle of the triangle m of the adjacent inner angle is 180, (ABC + ABD) = 180, then the angle ABC = (180 – 120) = 60.

Then, in a right-angled triangle ABC, the angle BAC = (90 – 60) = 30.

By condition, (AB + BC) = 15 cm, then AB = (15 – BC). (1).

The BC leg is located opposite an angle of 30, then AB = 2 * BC. (2).

Let’s solve the system of two equations, 1 and 2.

15 – BC = 2 * BC.

3 * BC = 15.

BC = 15/3 = 5 cm.

AB = 15 – 5 = 10 cm

Answer: The length of the hypotenuse is 10 cm.