That is Proof by Contradiction.
The famous one is the proof of the square root of 2 is irrational . First done by Euclid
Sasha is incorrect. you would add the 8x and the 3x not subtract them. Dante is correct because he adds 3x and 5x and he also adds 6 to both sides of the equation. Hope I helped!
The answer would be cos(52°)
They are alternate exterior angles. 1 is on the left side of the line and 20 would be on the opposite side of the line since 10 is.