Final answer:
Given that angle A is 30 degrees and the triangle's angles sum to 180 degrees, we might infer that this could be a 30-60-90 right triangle. However, due to the insufficient information about point M and without further clarification, we cannot determine the exact angles of triangle ABC with the details provided.
Step-by-step explanation:
The question we are addressing involves calculations related to the internal angles of triangle ABC. First, we are given that angle CAB measures 30 degrees. As for AM being twice the length of MC, we currently don't have enough information to use this detail effectively. We also have BC at 7 ft; however, without additional information about point M and its location, we can't make use of this measure in our calculations.
Using what we do know about the angles of a triangle - that they sum to 180 degrees - we can conclude that the other two angles must sum to 150 degrees (180 degrees - 30 degrees for angle CAB). If we assume that triangle ABC is a right triangle, this makes sense since angle C would likely be the right angle, as angles A and B are given as acute angles in the options. The ratios of the sides of a 30-60-90 triangle also align with the information given about AB being twice the length of MC. We can therefore conclude that the correct option would be: Angle A = 30 degrees, Angle B = 60 degrees, Angle C = 90 degrees.
However, without a specified point M and no additional information about the sides or angles, we can't confidently verify this with the information given. There may have been an oversight in the problem's formulation or in the details provided to us. This answer assumes a standard match with a 30-60-90 right triangle based on typical geometry principles.