∠2 and the angle marked 69° are congruent. The wake is a transversal across these parallel lines; ∠2 and the line adjacent to ∠1 will be corresponding angles, so they are congruent; similarly, the angle adjacent to ∠1 is a corresponding angle with the angle marked 69°. This gives us the equation
3x+y=69
Isolating y, we have y = 69 - 3x
We know that ∠2 and ∠1 are same-side interior angles, so they are supplementary; we also know that ∠2 = 69. This means that ∠1+69 = 180. Using the expression for ∠1, this gives us 3x+3y+69=180
Subtracting 69 from both sides we have 3x+3y=111
Substituting the value for y we isolated earlier, we have 3x+3(69-3x)= 111
Using the distributive property we have 3x+207-9x = 111
Combining like terms, -6x+207=111
Subtract 207 from both sides: -6x=-96
Divide both sides by -6: x = 16
Plug this into the equation we had for ∠2: y=69-3x y=69-3(16) y=69-48 y=21