We have two angles, x and y, that are supplementary.
x is the smaller angle and y is the larger angle.
If they are supplementary we can write:
[tex]x+y=180[/tex]The larger angle mesures 3 degrees more than twice the measure of the smaller angle.
Twice the smaller angle is 2x, so we can write:
[tex]y=2x+3[/tex]We can use the first equation to express y as a function of x and replace it in the second equation:
[tex]x+y=180\Rightarrow y=180-x[/tex]We can replace y and solve for x as:
[tex]\begin{gathered} y=2x+3 \\ 180-x=2x+3 \\ 180-3=2x+x \\ 177=3x \\ x=\frac{177}{3} \\ x=59\degree \end{gathered}[/tex]We can then calculate y as:
[tex]y=180-x=180-59=121\degree[/tex]Answer:
Smaller angle: x = 59°
Larger angle: y = 121°
