Identify the angles that each have a measure of 92 ( explain how you got these answers)i already guessed which ones are right but i need reasoning on how i “got” them

Angle 4 is 92 because of the Theorem about vertically opposite angles being equal (you can prove this theorem easily by argument of supplemental angles).

Angle 6 is 92 degrees because it is a similar angle to 2 (vertical lines are parallel).

Angle 7 is 92 degrees by the same argument as with angle 4 applied to angle 6.

let me know if you have questions