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.

 

 

\(x =\)

 

\(y =\)

 

\(\angle A =\) \(^{\circ}\)

 

\(\angle B =\) \(^{\circ}\)

 

\(\angle C =\) \(^{\circ}\)

 

\(\angle D =\) \(^{\circ}\)