The length of the rectangle exceeds twice its width by $1$ metre. If the area of the rectangle is $55 \mathrm{sq} \mathrm{m}$, find its length and width.

$AB$ and $CD$ are parallel. Prove that $m\angle APQ+m\angle CRQ=m\angle PQR$

$AB\parallel PQ, BC\parallel QR, \angle ABC=40°$. Find the measure of angle $PQR$.

$A$ and $B$ are midpoints of sides $PQ$ and $PR$ of $△PQR$, Prove $QR=2AB$.

Find the value of $x$ in the figure below:

State the measures of angles marked as $x$and $y$.

$ABCD$ is quadrilateral $P, Q, R$ and $S$ are midpoints of $AB, BC,CD$ and $DA$. Prove that $PQRS$ is a parallelogram.

Find the measures of the angles marked$x$ and $y$.

Find the measures of the angles marked $x$ and$y$.