Final answer:
The given equation 2(x + 7) = 2(2x + 8) produces a negative solution for x, which is unreasonable as angle measures cannot be negative. Therefore, it can be concluded that none of the provided answers is correct, and the equation may be incorrectly set up.
Step-by-step explanation:
To find the measure of each missing angle in the question provided, we need to solve the given equation and check if the solution is reasonable and makes sense with respect to the context, which in this case involves rotational motion and angle measurements.
We are given the equation 2(x + 7) = 2(2x + 8). To solve for x, we will simplify and equate both sides of the equation:
2x + 14 = 4x + 16
Subtract 2x from both sides:
14 = 2x + 16
Subtract 16 from both sides:
-2 = 2x
Divide both sides by 2:
-1 = x
However, an angle measure cannot be negative, which means that based on the given equation, there might be a mistake, or the context provided does not support this solution. Therefore, we conclude that none of the answers provided (A, B, C) are correct.
The step involving the check of the solution's reasonableness is crucial. Since the solution yielded a negative angle, which does not make sense in a practical context, we determine that the answers provided within the question do not reflect the correct angle measures, and the equation might be incorrectly set up.