Final answer:
The measure of angle 2 is presented as m₂ = x. Without further context or constraints, the exact value cannot be determined from the given options. Additional information about the relationship between these angles or the larger geometric figure they belong to is required.
Step-by-step explanation:
The problem gives us two angles where m₁ = m₂ and m₇ = 2x, also given that m₂ = x. The question asks for the measure of angle 2, which is represented as m₂.
To find the value of x, we can use the information given. Firstly, since m₁ = m₂ and m₂ = x, angle 2 is already given as x degrees. Secondly, as m₇ = 2x, we need to consider what x could be based on the options provided: 30°, 60°, 90°, or 120°. Without additional context or constraints, we cannot definitively determine the value of x. It's possible this question is part of a larger problem involving supplementary or complementary angles, or angles within a particular geometric figure.