# Given a triangle ABC. External angle at apex B 150 degrees, AC + AB = 12 cm. Find the length of the hypotenuse.

September 30, 2021 | education

| The angle ABC is adjacent to the angle ABD, the sum of which is 180, then the angle ABC = (180 – ABD) = (180 – 150) = 30.

The AC leg lies opposite an angle of 30, then its length is equal to half the length of the hypotenuse AB.

AC = AB / 2.

By condition, AC + AB = 12 cm, then AB / 2 + AB = 12.

1.5 * AB = 12 cm.

AB = 12 / 1.5 = 8 cm.

Answer: The length of the hypotenuse AB is 8 cm.

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