Let angle 1, angle 2, and angle 3 have the following relationships. Angle 1 and 2 are acute vertical angles
Angle 3 is an obtuse angle adjacent to both angle 1 and angle 2.
What is the sum of the measure of angle 1 and the measure of angle 3?

180 degrees

Vertical angles are opposite angles that share only a vertex. Since ∠3 is adjacent to both ∠1 and ∠2, this means that ∠3 shares a side and vertex with both of these angles.
This means that ∠3 and ∠1 form a straight line; this makes them a linear pair, which makes their sum 180°.