Supplementary Angles
Supplementary angles are two angles whose measures add up to 180°. When two supplementary angles are given and their difference in measure is known, we can determine the measure of each angle.

Given Information
Let's denote the larger angle as \(x\) and the smaller angle as \(y\). We are given that the two angles are supplementary, so we have the equation:
\[x + y = 180\]
We are also given that the two angles differ by 40°, which means:
\[x - y = 40\]

Solving the Equations
We can solve the system of equations by adding the two equations together to eliminate \(y\):
\[x + y + x - y = 180 + 40\]
\[2x = 220\]
\[x = 110\]
Now that we have found the measure of the larger angle, we can substitute this back into one of the original equations to find the measure of the smaller angle:
\[110 + y = 180\]
\[y = 70\]

Conclusion
Therefore, the measure of the larger angle is 110°. The smaller angle is 70°. This solution satisfies both the condition that the angles are supplementary and that their difference is 40°.

The correct answer is 110.