In a cyclic quadrilateral,$\angle A = 3x + 15^{\circ}$ and $\angle C = 2x + 15^{\circ}$. Find the value of $x$.

In cyclic quadrilateral $PQRS$,if $\angle PRQ = 52^{\circ}$,then find $\angle PSQ$. (in $^{\circ}$)

$ABCD$ is a parallelogram. The circle passing through $A, B$ and $C$ intersects $CD$ (produced if necessary) at $E$. Prove that $AE = AD$.

In a cyclic quadrilateral $PQRS$,$\angle QPR = 40^{\circ}$ and $\angle PSQ = 70^{\circ}$,then find $\angle PQR$. (in $^{\circ}$)

$ABCD$ is a cyclic quadrilateral. If $AB \parallel CD$,then prove that $BC = AD$.

In cyclic quadrilateral $ABCD$,if $5 \angle A = 13 \angle C$,then find $\angle A$. (in $^{\circ}$)