Given a cyclic quadrilateral
The sum of the opposite angles = 180
so,
[tex]\begin{gathered} 2y+90=180 \\ (5x-1)+76=180 \end{gathered}[/tex]solve the first equation to find y as follows:
[tex]\begin{gathered} 2y=180-90 \\ 2y=90 \\ y=\frac{90}{2}=45 \end{gathered}[/tex]Solve the second equation to find x as follows:
[tex]\begin{gathered} 5x-1+76=180 \\ 5x+75=180 \\ 5x=180-75 \\ 5x=105 \\ x=\frac{105}{5}=21 \end{gathered}[/tex]so, the answer will be:
x = 21
y = 45
