Final answer:
To determine the measures of angles AMC and DMC in triangle AMD, we can use the fact that the sum of the angles in a triangle is 180 degrees. By setting up equations for each angle and solving them, we can determine the measures.
Step-by-step explanation:
In triangle AMD, the sum of angles must be 180 degrees. Therefore, we can write the equation 3x + 6 + 8x - 49 + ACM = 180, where ACM represents the angle AMC. Simplifying the equation, we get 11x - 43 + ACM = 180. Next, we need to find the measure of ACM, so we will isolate it by subtracting 11x - 43 from both sides of the equation. ACM = 180 - 11x + 43. Similarly, we can find the measure of DMC by using the equation 3x + 6 + 8x - 49 + DMC = 180. Solving for DMC in the same way, we get DMC = 180 - 11x + 43.