Final answer:
The two angles are supplementary, with one being 150° and the other being 30°, because the smaller angle is 20% of the larger angle and they must add up to 180°.
Step-by-step explanation:
When two angles are supplementary, their measures add up to 180°. Given that one angle is 20% of the other, let's denote the larger angle as x and the smaller angle as 0.20x. The equation modeling this relationship would be:
x + 0.20x = 180°
This simplifies to:
1.20x = 180°
Solving for x gives:
x = 180° / 1.20
x = 150°
Now to find the measure of the other angle, we multiply the larger angle x by 20%:
0.20x = 0.20 × 150°
0.20x = 30°
Thus, the two supplementary angles are 150° and 30°.