Since the sum of angles of a triangle is 180 degrees
Since the measures of the 3 angles of the 1st triangle are
[tex](x-7)^{\circ},(y+10)^{\circ},84^{\circ}[/tex]Add them and equate the sum by 180 degrees
[tex]x-7+y+10+84=180[/tex]Add the like terms on the left side
[tex]\begin{gathered} x+y+(-7+10+84)=180 \\ x+y+87=180 \end{gathered}[/tex]Subtract 87 from both sides
[tex]\begin{gathered} x+y+87-87=180-87 \\ x+y=93\rightarrow(1) \end{gathered}[/tex]Since the measures of the 3 angles of the other triangles are
[tex](x+30)^{\circ},47^{\circ},49^{\circ}[/tex]Add them and equate the sum by 180 degrees
[tex]x+30+47+49=180[/tex]Add the like terms on the left side
[tex]\begin{gathered} x+(30+47+49)=180 \\ x+126=180 \end{gathered}[/tex]Subtract 126 from both sides
[tex]\begin{gathered} x+126-126=180-126 \\ x=54 \end{gathered}[/tex]Substitute the value of x in equation (1) to find y
[tex]54+y=93[/tex]Subtract 54 from both sides
[tex]\begin{gathered} 54-54+y=93-54 \\ y=39 \end{gathered}[/tex]The answers are:
x = 54
y = 39
