Final answer:
To find the measures of the three angles, use the fact that the sum is 180 degrees and set up an equation.
Step-by-step explanation:
To find the measures of the three angles, let's denote the first angle as x. The second angle will be 2x since the sum of the second and third angles is twice the measure of the first angle. The third angle will be x + 12, as it is twelve more than the second angle.
Since the sum of the angles of a triangle is 180 degrees, we can set up an equation: x + 2x + (x + 12) = 180.
Simplifying the equation, we get 4x + 12 = 180. Solving for x, we find x = 42. Thus, the measures of the three angles are: first angle = 42 degrees, second angle = 84 degrees, and third angle = 96 degrees.
Learn more about Triangle angles