It should be noted that the diagonals of a rectangle bisect each other and the diagonals are equal
From the given, the diagonals of the rectangle QUVX are QV and UX
Given
[tex]\begin{gathered} QV=3x+13 \\ XU=7x-11 \end{gathered}[/tex]
Since the diagonals are equal, then
[tex]\begin{gathered} QV=XU \\ 3x+13=7x-11 \\ 3x-7x=-11-13 \\ -4x=-24 \\ x=\frac{-24}{-4} \\ x=6 \end{gathered}[/tex]
Also, note that all angles in a rectangle are 90 degrees. Then
[tex]m\angle QXV=m\angle\text{XVU}=m\angle\text{VUQ}=m\angle\text{UQX}=90^0[/tex]
Given
[tex]m\angle\text{QXV}=10y-10[/tex]
So,
[tex]\begin{gathered} 90^0=10y-10 \\ 90+10=10y \\ 100^0=10y \\ 10y=100^0 \\ \frac{10y}{10}=\frac{100^0}{10} \\ y=10^0 \end{gathered}[/tex]
Hence, x = 6
y= 10⁰
