Answer :
In general, two angles are supplementary if their addition is equal to 180°; therefore, in our case, if x is the angle we need to find and y is its supplement,
[tex]\begin{gathered} x+y=180 \\ \end{gathered}[/tex]Furthermore, according to the problem,
[tex]\begin{gathered} x=5y \\ \Rightarrow y=\frac{x}{5} \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow x+\frac{x}{5}=180 \\ \Rightarrow\frac{6x}{5}=180 \\ \Rightarrow150 \end{gathered}[/tex]Therefore, the answer to part a) is 150°
b) Two angles are complementary if their addition is equal to 90°, and the sum of the three interior angles of a triangle is 180°; thus, in our case, if z is the third angle,
[tex]\begin{gathered} z+x+y=180 \\ \Rightarrow z+90=180 \\ \Rightarrow z=90 \end{gathered}[/tex]