Final answer:
The measures of the two supplementary angles are 45° and 135°, with the smaller angle being one-third the size of the larger angle.
Step-by-step explanation:
When two angles are said to be supplementary, their measures add up to 180°. If one angle is three times as large as the other, we can represent the smaller angle as 'x' and the larger angle as '3x'. Therefore, the equation to represent their relationship would be x + 3x = 180°.
Combining like terms, we get 4x = 180°. To find the value of 'x', we divide both sides of the equation by 4, which results in x = 45°. This means the smaller angle is 45° and the larger angle is 3 times 45°, which is 135°.
After calculation, we can conclude that the measures of the two supplementary angles are 45° and 135° respectively.