Jharne De and Ranjana Kumar Solutions for Chapter: Quadrilaterals, Exercise 4: HOTS (Higher Order Thinking Skills)

$ABCD$ is a square. Its diagonal $AC$ and $BD$ intersect each other at $O$. Find the measures of $\angle CAD$and $\angle DBC$.

The size of the obtuse angles of a rhombus is twice the size of its acute angle. Find the acute angle. (Write the answer without degree)

The diagonals of rhombus $ABCD$ intersect at $O$. If $AC=12 \mathrm{cm}$ and $BD=16 \mathrm{cm}$, find the length of its side.

In the figure, $PQRS$ is a square and $PQTU$ is a rhombus. $\angle UPS=136°$. Find $x$ and $y$.

$ABCD$ is a square. $P, Q, M, N$ are mid points of the sides on which they lie. Prove that $PQ=MN$.

In the following figure, $PQRS$ is a trapezium with $PQ\parallel RS$. The bisectors of $\angle P$ and $\angle Q$ meet at $M$ on side $RS$ such that $\angle PMQ = 80°$. If $PM = QM$, then show that $\angle S+\angle R=160°$.

In the following figure, $ABCD$ is a rectangle. The bisector of $\angle B$ meets side $CD$ at $E$ such that $BC=EC$. Find the measure of $\angle BED$ and $\angle EBA$.

In the following figure, $PQRS$ is an isosceles trapezium with $PQ\parallel RS$. Find the measure of side $PQ$.