VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

In a parallelogram $ABCD$, the bisector of $\angle A$ also bisects $BC$ at $X$.  Find $AB:AD$.

In the given figure $PQRS$ is an isosceles trapezium. If the measurement of $x$ is $k°$, then find the value of $k$.

In the given figure $ABCD$ and $AEFG$ are two parallelograms. If $\angle C=58°,$ and the measure of $\angle F$ is $k°$, then find the value of $k$.

In a quadrilateral $ABCD,$ bisectors of angles $A$ and $B$ intersect at $O$ such that $\angle AOB=75°$. If the value of $\angle C+\angle D$ is $k°$, then find the value of $k$.

The diagonals of a rectangle $ABCD$ meet at $O$. If $\angle BOC=44°$. If the measure of $\angle OAD$ is $k°$, then find the value of $k$.

If $ABCD$ is a rectangle with $\angle BAC=32°$ and the measure of $\angle DBC$ is $k°$, then find the value of $k$.

If the bisectors of two adjacent angles $A$ and $B$ of a quadrilateral $ABCD$ intersect at a point $O$ such that $\angle C+\angle D=k\angle AOB$, then find the value of $k$.

In the given figure, $ABCD$ is a rectangle in which diagonal $AC$ is produced to $E$ If $\angle ECD={146}^{°},$ find $\angle AOB$.