Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$. The fourth angle is (in $^{\circ}$)

In quadrilateral $ABCD$,the angles are in the ratio $\angle A : \angle B : \angle C : \angle D = 2 : 4 : 5 : 7$. Find the measure of each angle of the quadrilateral and state the type of quadrilateral $ABCD$.

In quadrilateral $ABCD$,$AC = BD$ and $AC \perp BD$. If $P, Q, R$ and $S$ are the midpoints of the sides $AB, BC, CD$ and $DA$ respectively,prove that $PQRS$ is a square.

In the figure,$ABCD$ and $AEFG$ are two parallelograms. If $\angle C = 55^{\circ},$ determine $\angle F.$ (in $^{\circ}$)

$E$ is the mid-point of a median $AD$ of $\triangle ABC$ and $BE$ is produced to meet $AC$ at $F$. Show that $AF = \frac{1}{3} AC$.

Can all the angles of a quadrilateral be right angles? Give reason for your answer.