Angles were actually my favorite geometry unit! So I’m going to go ahead and explain how to do this, but you can ask me for more help if needed.
Angle 1: It is vertical to angle 3, which is a right angle. If right angles are equal to 90 degrees and vertical angles are congruent, than angle 1 must be equal to…
Angle 2: This one is a tiny bit more complicated there’s a lot of reasons and explanations for this one, but I’m going to go with a simple one. Angle 3 is supplementary to angle 2 plus 75 degrees. And since we already know angle 3 is equal to 90 degrees and supplementary angles are equal to 180 degrees, we can deduct that 90-75 is equal to angle 2.
Angle 3: We have already established that this is equal to 90 because it’s a right angle.
Angle 4: Once again, a few ways we can solve this. I’ll just pick one, though. Angle 4 plus 30 degrees is vertical, therefore equal to 75 degrees. Sooo angle 4 is equal to 75-30.
Angle 5: Congrats, you’ve made it to the last one! Since this is vertical to angle to and we’ve already solved for that, it is equivalent to the value of angle 2!
Hope this helps! Comment if you have questions.