In the given figure, $KLMN$ is a rectangle. $P, Q, R, S$ are the midpoints of $KL, LM, MN \mathrm{and} NK$ respectively. Find $k$, if $\angle KPS=30°, \angle QRS=k°$.

In the figure above, $PQRS$ is a trapezium, $PQ\parallel SR, QR=RS, \mathrm{and} \angle QRS=90°$. $QR=24 \mathrm{cm} \mathrm{and} PS=25 \mathrm{cm}$. Find $k$, if the length of $PQ$ is $k \mathrm{cm}$.

The sum of $3$ distinct angles of a triangle is equal to the sum of $2$ right angles and the difference between two pairs of the angles is $10°$. Find $k$, if the smallest amongst the angles is $k°$.

$P$ is an interior point of a square $ABCD$. Prove that $PA+PB+PC+PD>2AB$.

How can you draw a circle that passes through four vertices of a rectangle? Explain.

In the given figure, $PQRS$ is a parallelogram and $G$ is the centroid of the triangle $PQR$. $A$ is the point of intersection of the diagonals$PR \mathrm{and} SQ$. If $AG=3 \mathrm{cm} \mathrm{and} SQ=k \mathrm{cm}$, find $k$, if the perimeter of the rhombus $ABCD$ is $k \mathrm{cm}$.

In the given figure, $ABCD$ is a square of side $18 \mathrm{cm}$ and $PN\perp BC \mathrm{and} PM\perp AB$.  Find $k$, if the length of $MN$ is $k\sqrt{2} \mathrm{cm}$.

$ABCD$ is a kite in which $AB=AD$ and $CB=CD$. $\angle ABD=30° \mathrm{and} \angle BDC=40°$. Find $k$, if  $\angle A+\angle C=k°$.

Find $k$, if the complement of an angle whose supplement is $100°$ is $k°$.