Based on Triangle Angle Sum Theorem, the sum of the angles inside a triangle must equal 180°.
Use the equation 2x + 4x + 6x = 180° to solve the measures of the angles in this triangle.
2x + 4x + 6x = 180°
12x = 180°
x = 15°
Now, plug x back into the equations to find the measure of each angle:
Angle 1: 2x = 2(15) = 30°
Angle 2: 4x = 4(15) = 60°
Angle 3: 6x = 6(15) = 90°
Therefore, the measures of the angles in this triangle are 30°, 60°, and 90°.