The equations $\frac{2}{3} x + \frac{3}{2} y = 5$ and $\ldots \ldots \ldots$ are the same.

Do the following equations represent a pair of coincident lines? Justify your answer.
$-2x - 3y = 1$
$6y + 4x = -2$

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.

The length of a rectangle is one and a half times its breadth. If the perimeter of the rectangle is $100 \,cm$, find the length and the breadth of the rectangle.

There are some students in the two examination halls $A$ and $B$. To make the number of students equal in each hall,$10$ students are sent from $A$ to $B$. But if $20$ students are sent from $B$ to $A$,the number of students in $A$ becomes double the number of students in $B$. Find the number of students in the two halls.

$ABCD$ is a cyclic quadrilateral (see Figure). Find the angles of the cyclic quadrilateral.