Given:
Let x and y denote the supplementary angles.
Given that an angle measures 102.8° more than the measure of its supplementary angles.
This can be written in expression as,
[tex]y=102.8^{\circ}+x[/tex]
Measure of two angles:
Since, the two angles are supplementary and the supplementary angles add up to 180°
Thus, we have;
[tex]x+y=180^{\circ}[/tex]
Substituting [tex]y=102.8^{\circ}+x[/tex] in the above formula, we get;
[tex]x+102.8^{\circ}+x=180^{\circ}[/tex]
[tex]2x+102.8^{\circ}=180^{\circ}[/tex]
[tex]2x=77.2^{\circ}[/tex]
[tex]x=38.6^{\circ}[/tex]
Thus, the measure of one angle is 38.6°
Substituting [tex]x=38.6^{\circ}[/tex] in the equation [tex]y=102.8^{\circ}+x[/tex], we get;
[tex]y=102.8^{\circ}+38.6^{\circ}[/tex]
[tex]y=141.4^{\circ}[/tex]
Thus, the measure of the other angle is 141.4°
Hence, the measure of the two angles are 38.6° and 141.4°
