This is a right angle so it's 90 degrees. Angle 1 and angle 2 add to 90.
Angle 1 = x+2. Angle 2 = 7x.
So let's add those two angles and set them equal to 90.
(x+2) + 7x = 90
Now solve for x.
8x + 2 = 90
8x = 88
x = 11
Substitute x = 11 back into the equations for Angle 1 and Angle 2 (given in the problem) to find the measures of these angles.
Angle 1 = x+2 = 11+2 = 13 degrees.
Angle 2 = 7x = 7*11 = 77 degrees.
Let's do a quick check - - - angle 1 + angle 2 should equal 90!
13 + 77 = 90.