Final answer:
Angle AMH measures 54 degrees, which is found by solving the equation created by setting twice the measure of angle TMH equal to the measure of angle AMH. The given options do not include the correct answer, suggesting a potential error in the expressions or options provided.
Step-by-step explanation:
The student is asking to find the measure of angle AMH given that MT bisects AMH and the expressions for angles TMH and AMH in terms of x are provided. Since MT bisects AMH, angle TMH is equal to half of angle AMH. Therefore, we can set up an equation with the expressions given: 2(8x + 1) = 15x + 9. Simplifying and solving for x gives us x = 3. Substituting x back into the expression for angle AMH (15x + 9), we find that angle AMH is 54 degrees.
However, the options given (A. 42°, B. 36°, C. 45°, D. 39°) do not contain the correct answer. The calculation shows that the measure of angle AMH is 54 degrees, which is not listed among the options. Therefore, the student should verify the options given or check if there was a mistake in the provided expressions for the angles.