To determine the measure of angle ∠2 based on the given measure of angle ∠4, we need to know the relationship between these angles—whether they are complementary, supplementary, or part of a different geometric configuration (such as vertical angles).
Assuming that angles ∠4 and ∠2 are supplementary (which is common in many problems), we find m∠2 by using the following formula:
m∠2 + m∠4 = 180°
Given that m∠4 = 31°, we can substitute:
m∠2 + 31° = 180° m∠2 = 180° - 31° m∠2 = 149°
However, none of the provided options (90°, 31°, 180°, 59°) match this answer.
If ∠4 and ∠2 are complementary instead, we would use:
m∠2 + m∠4 = 90°
Substituting:
m∠2 + 31° = 90° m∠2 = 90° - 31° m∠2 = 59°
Since 59° is one of the choices you provided, that would be the answer if they are complementary:
m∠2 = 59°