Final answer:
To find the measures of the angles x, 2x, and 3x in a triangle, use the fact that the sum of the angles in a triangle is always 180 degrees and solve the equation x + 2x + 3x = 180, giving x = 30 degrees.
Step-by-step explanation:
If the measures of the angles of a triangle are x, 2x, and 3x, we can find the measure of each angle by using the fact that the sum of the angles in any triangle adds up to 180 degrees. We set up the equation x + 2x + 3x = 180, which simplifies to 6x = 180. Dividing both sides by 6 gives us x = 30 degrees. Consequently, the angles of the triangle measure 30 degrees, 60 degrees (2x), and 90 degrees (3x).