∠1, ∠2, and ∠3 add up to one full turn, or 360°. We can write this fact as the equation
∠1 + ∠2 + ∠3 = 360
∠1 is given to us as a right angle - 90° - and the values ∠2 and ∠3 are given in the question, so we can rewrite our equation with that information as
90 + (x - 7) + 2x = 360
Which we can then solve for x:
x - 7 + 2x = 270 (subtract 90 from both sides)
3x - 7 = 270 (combine like terms)
3x = 277 (add 7 to both sides)
x = 277/3 = 92 1/3 (divide both sides by 3)
Since ∠3 = 2x, we can multiply our result by 2 to find that ∠3 = 2 x (92 1/3) = 184 2/3°
