I think your work was right, except you mixed up or lost track of a sign.
7x+5 = 14x-16
subtract 7x and add 16 to both sides:
21 = 7x
divide by 7
3 = x
Now substitute that back into either of angle 1 or angle 2 to find the measure of those. (They'll be the same.)
Then use the fact that angle 1 and angle 2 form a straight line and add up to 180ยบ.