Let's just compare the angles to start - - - these are two parallel lines cut by another line (transversal), so there are a lot of equal angles.
Angles 1 and 5 are the same
Angles 2 and the 65 degree angles are the same.
Angles 4 and 8 are the same.
And 3 and 7 are the same.
There are even more similar angles:
1 and 3 are the same. 2 and 4 are the same.
5 and 7 are the same, and 8 and the 65 degree angle are the same.
So without any math, Angles 2, 4 and 8 are all 65 degrees.
So Angle 65 + Angle 5 = 180. Therefore Angle 5 = 115.
Therefore angle 7 is 115. (You could also say that 65+ Angle 7 = 180.)
Since angle 7 is 115, so is angle 3 and angle 1.
So in conclusion
Angle 1: 115
Angle 2: 65
Angle 3: 115
Angle 4: 65
Angle 5: 115
Angle 7: 115
Angle 8: 65