Final answer:
To find the measures of the two angles, assume the measure of the supplementary angle is x degrees. Use the sum of angles in a triangle to set up an equation and solve for x. Hence, the measure of the two angles are 154° and 26°.
Step-by-step explanation:
To find the measures of the two angles, let's assume that the measure of the supplementary angle is x degrees. According to the given information, one angle measures 128° less than the measure of the supplementary angle. So the other angle is x - 128°.
We know that the sum of two supplementary angles is 180°. Therefore, we can set up the following equation: (x) + (x - 128°) = 180°.
Simplifying the equation, we have: 2x - 128° = 180°. Adding 128° to both sides, we get: 2x = 308°. Finally, dividing both sides by 2, we find that x = 154°.
So the measure of the supplementary angle is 154°, and the other angle is 154° - 128° = 26°.