Final answer:
The question requires solving for x using the properties of midsegments, but the provided information is insufficient to give a solution. A midsegment connects the midpoints of two sides of a triangle, paralleling the third side and half its length. Normally, the Triangle Midsegment Theorem would be applied.
Step-by-step explanation:
The question asks to solve for x in a geometrical context where lines that appear to be midsegments are indeed midsegments. A midsegment in a triangle is a segment connecting the midpoints of two sides and it is parallel to the third side and half its length.
To solve for x, we would typically use properties of midsegments and the information given such as angles or lengths. However, the information provided in the question is insufficient to provide a detailed solution because the relationship between the angle measures 45°, (7x-8)°, 80° and the midsegments is not described. Normally, with more context, we could apply the Triangle Midsegment Theorem or other geometric properties and principles to find the value of x.