ABCD is a cyclic quadrilateral .find …

We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°.
{tex}\therefore{/tex} {tex}\angle{/tex}A + {tex}\angle{/tex}C = 180°
{tex}\Rightarrow{/tex} 4y + 20 - 4x = 180°
{tex}\Rightarrow{/tex} -4x + 4y = 160°
{tex}\Rightarrow{/tex} x - y = -40° ....(1)
 Also {tex}\angle{/tex}B + {tex}\angle{/tex}D = 180°
{tex}\Rightarrow{/tex} 3y - 5 - 7x + 5 = 180°
{tex}\Rightarrow{/tex} -7x + 3y = 180°............... (2)
Multiplying equation (1) by 3, we obtain:
3x - 3y = -120° ..... (3)
Adding equations (2) and (3), we obtain:
-4x = 60°
{tex}\Rightarrow{/tex} x = -15°
Substituting the value of x in equation (1), we obtain:
-15 - y = 40°
{tex}\Rightarrow{/tex} y = -15 + 40 = 25°
{tex}\therefore{/tex} {tex}\angle{/tex}A = 4y + 20 = 4 {tex}\times{/tex} 25 + 20 = 120°
{tex}\angle{/tex}B = 3y - 5 = 3 {tex}\times{/tex} 25 - 5 = 70°
{tex}\angle{/tex}C = -4x = -4 {tex}\times{/tex} (-15) = 60°
{tex}\angle{/tex}D = -7x + 5 = -7(-15) + 5 = 110°