Since the angles are supplementary, you know their sum is 180°. You are told their difference is 40°. The solution to a sum and difference problem is always the same: the larger number is the average of the given ones; the smaller number is that less the difference.
Angle 2 is largest so its measure is
... m∠2 = (180°+40°)/2 = 110°
... m∠1 = 110° -40° = 70°
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Here's the generic solution to a "sum and difference" problem. Let the sum be represented by s, and the difference represented by d. Then the two values a and b satisfy ...
... a + b = s
... a - b = d
Add these two equations to get
... 2a = s+d
... a = (s+d)/2
The second of the orginal equations can be solved for b:
... b = a - d . . . . . add b-d to the equation
Or, you can subtract the second eqution from the first ...
... 2b = s - d
... b = (s-d)/2