Respuesta :
ANSWER
Part A:
[tex]\begin{gathered} x=10^0 \\ m\angle1=40^0 \\ m\angle2=50^0 \end{gathered}[/tex]Part B:
[tex]\begin{gathered} x=30^0 \\ m\angle1=150^0 \\ m\angle2=30^0 \end{gathered}[/tex]EXPLANATION
Part A: Complementary
Two angles are said to be Complementary if there sum is 90 degrees.
[tex]\begin{gathered} m\angle1\text{ + m}\angle2\text{ = 90} \\ 30\text{ + x + 40 + x = 90} \\ 2x\text{ + 70 = 90} \\ 2x\text{ = 90 - 70} \\ 2x\text{ = 20} \\ x\text{ = }\frac{20}{2}\text{ = 10} \end{gathered}[/tex]Measure of the two angles
[tex]\begin{gathered} m\angle1\text{ = 30 + x} \\ m\angle1\text{ = 30 + 10} \\ m\angle1=40^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle2\text{ = 40 + x} \\ m\angle2\text{ = 40 + 10} \\ m\angle2=50^0 \end{gathered}[/tex]Part B: Supplementary
Two angles are said to be Supplementary if there sum is 180 degrees
[tex]\begin{gathered} m\angle1\text{ + }m\angle2\text{ = 180} \\ 5(m\angle2)\text{ + x = 180} \\ 5x\text{ + x = 180} \\ 6x\text{ = 180} \\ x\text{ = }\frac{180}{6}=30^0 \end{gathered}[/tex]Measure of the two angles
[tex]\begin{gathered} m\angle1\text{ = 5(m}\angle2) \\ m\angle1\text{ = 5x} \\ m\angle1\text{ = 5 }\times30 \\ m\angle1=150^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle2\text{ = x} \\ m\angle2=30^0 \end{gathered}[/tex]