Angle Sum Property of a Quadrilateral

If the sides $BA$and $DC$of quadrilateral $ABCD$ are produced as shown in the given figure, then

Read the statements carefully and state $‘T\text{'}$for true and $‘F’$for false.
(i) Diagonals of a parallelogram are perpendicular to each other.
(ii) All four angles of a quadrilateral can be obtuse angles.
(iii) If all sides of a quadrilateral are equal, then it is a rhombus.

By using a given figure of quadrilateral $ABCD,$ match the following:

Column-I Column-II
(P) If ABCD is a Parallelogram (1) $25°$
then sum of the angles $X,YandZ$
is-
(Q) If ABCD is a rhombus (2) $180°$
where $\angle D=130°$, then
the value of $X$ is
(R) If ABCD is a rhombus, the (3) $50°$
value of $\mathrm{W}$ is
(S) If $ABCD$ is a Parallelogram, (4) $90°$
where $x+\mathit{}y=130°,$then the
value of $\angle B$ is

The measure of all the angles of a parallelogram, if an angle adjacent to the smallest angle is $24°$ less than twice the smallest angle is

In a quadrilateral $ABCD$, the lines segments bisecting $\angle C$ and $\angle D$ meet at $E$.Then $\angle A+\angle B$ is equal to _____.

Two adjacent angles of a parallelogram are in the ratio $2:3$. The angles are

If the angles of a quadrilateral are $X,X+20°,X-40°$ and $2X$. Then, the difference between greatest angle and the smallest angle is $\_\_\_\_\_\_\_\_\_\_$.

The diagonals $AC$ and $BD$of a parallelogram $ABCD$intersect each other at the point $O$. If $\angle DAC=32°$ and $\angle AOB=\mathrm{}70°$, then
$\angle DBC$ Is equal to $\_\_\_\_\_\_$.

If the angles of a quadrilateral are in the ratio $1:2:3:4$. Then, the measure of angles in descending order are