$ABCD$ is a cyclic quadrilateral in which $\angle A = 80^{\circ}$ and $\angle B = 75^{\circ},$ then $\angle D = \dots$ (in $^{\circ}$)

In the figure,$ABCD$ is a cyclic quadrilateral in which $AC$ and $BD$ are its diagonals. If $\angle DBC = 55^{\circ}$ and $\angle BAC = 45^{\circ}$,find $\angle BCD$. (in $^{\circ}$)

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

$ABCD$ is a cyclic quadrilateral in which $\angle BAC = 45^{\circ}$ and $\angle ADB = 55^{\circ},$ then $\angle ABC = \dots$ (in $^{\circ}$)

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

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