What is the value of x if the acute angles of a right triangle measure 8x and 12x?

A triangle equals 180°. A right triangle has a 90° angle. So the other two angles added together will also need to equal 90°.

8x + 12x = 90°

20x = 90°

Divide both sides by 20.

x = 4.5°

Then plug in the answer for x into the other two angles.

8x=

8 (4.5) = 36°

12x=

12 (4.5) = 54°

Check your answer:

8x + 12x = 90°

36° + 54° = 90°