The angles ∠1 and ∠2 are vertical angles, therefore, their measures are equal.
If we find the measure of ∠1, we find the measure of ∠2.
The sum of the inside angles of a triangle add up to 180º, this gives to us the following equation
[tex]47+57+m\angle1=180[/tex]
Solving for the measure of ∠1, we have our answer
[tex]m\angle2=76[/tex]
