First, assign a variable that represents the measure of the smaller angle. Let it be x.
Since the larger angle is 44 more that the measure of the smaller angle, then the other angle is x +44.
Since the two angles x and x+44 are supplementary, to determine their values, take the sum of these two and set it equal to 180.
`x + x +44=180`
So, the measure smaller of the smaller angle is 68 degrees.
To get the measure of the larger angle, plug-in x=68 to x+44.
Hence, the measure of the two angles are 68 and 112 degrees.