Final answer:
Without additional context such as a diagram, it is not possible to accurately determine m₄. Assuming m₃ and m₄ are supplementary, m₄ would equal 115°, which is not among the given options.
Step-by-step explanation:
The question is asking to find the measure of angle m₄ given the measures of angles m₁ and m₃. In usual geometrical problems, adjacent angles that sum up to 180° are considered supplementary. Given that m₁ = 45° and m₃ = 65°, we can infer that angle m₄ is supplementary to angle m₃ if they are adjacent. Therefore, we can calculate the measure of m₄ by subtracting m₃ from 180°:
m₄ = 180° - m₃
m₄ = 180° - 65°
m₄ = 115°
However, this result does not match any of the provided options. Without further context, such as a diagram or additional information about the relationship between the angles, we cannot definitively determine m₄. The result of 115° suggests that either there is a mistake in the options or additional geometrical relationships need to be considered to solve the problem correctly.