Understanding Q...

PQRS is a parallelogram whose diagonals intersect at M.
If $$\angle PMS = 54^{\circ}$$, $$\angle QSR = 25^{\circ}$$ and $$\angle SQR = 30^{\circ}$$: find $$\angle RPS $$

PQRS is a parallelogram whose diagonals intersect at M.
If $$\angle PMS = 54^{\circ}$$, $$\angle QSR = 25^{\circ}$$ and $$\angle SQR = 30^{\circ}$$: find $$\angle PRS$$

In parallelogram PQRS $$\angle Q = (4x-5)^{\circ}$$ and $$\angle S = (3x+10)^{\circ}$$. Calculate $$\angle Q$$ 

Find the number of sides in a regular polygon, if its each interior angle is $$160^{\circ}$$.

The perimeter of a parallelogram $$ABCD= 40$$ cm, $$AB= 3x$$ cm, $$BC= 2x$$ cm and $$CD= 2\left ( y\, +\, 1 \right )$$ cm. Find the values of $$x$$ and $$y$$.

In parallelogram $$ABCD$$, $$AP$$ and $$AQ$$ are perpendiculars from vertex of obtuse angle $$A$$ as shown in the figure. If $$\angle x\, :\, \angle y= 2\, :\, 1$$; find smallest angles of the parallelogram.(in degrees)

In the given figure, $$E$$ is mid-point of $$AB$$ and $$DE$$ meets diagonal $$AC$$ at point $$F$$. If $$ABCD$$ is a parallelogram and area of  $$\bigtriangleup ADF$$ is $$60 \: cm^{2}$$, then area of parallelogram $$ABCD$$ is

Find the value of $$x , y$$

the area of $$\triangle ABE$$?

In a quadrilateral ABCD, if AB || CD, $$\angle$$D $$= 2\angle$$B, AD = b and CD = a, then the side AB is of length: