For this case, the first thing you should know is that by definition, the vertical angles are congruent.
We have then:
∠1 and ∠2 are vertical angles.
Therefore, by definition:
∠1 = ∠2
On the other hand we have:
∠2 has a measure of 31 °.
Thus:
∠1 = ∠2 = 31 °
Answer:
the measure of ∠1 is:
∠1 = 31 °
