Find the measures of supplementary angles 1 and 2, if: m∠1 is less than m∠2 by 40° include your explanation

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°

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

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