54. Exemplar problems XX

The angles of a cyclic quadrilateral $ABCD$ are $\angle A = (6x + 10)^{\circ}$, $\angle B = (5x)^{\circ}$, $\angle C = (x + y)^{\circ}$, $\angle D = (3y - 10)^{\circ}$.

 

Find $x$ and $y$, and hence the values of the four angles.

 

 

$x =$

 

$y =$

 

$\angle A =$ $^{\circ}$

 

$\angle B =$ $^{\circ}$

 

$\angle C =$ $^{\circ}$

 

$\angle D =$ $^{\circ}$