Hello, dolly kohli!
Obviously, some information is missing . . .
can you solve this sum for me --- sum?
PQRS is a quadrilateral.
Sides RS and QR are the same length.
Sides QP and RS are parallel.
Calculate:
$\displaystyle 1)\;\angle SQR\qquad 2)\;\angle PSQ\qquad 3)\;\text{ length }PQ \qquad 4)\;\text{ length }PS \qquad 5)\;\text{ Area of }PQRS$
With no more information, it is impossible to answer the questions . . .
Code:
P Q
o * * * * * * * * * o
θ * *
* θ *
* * *
* * *
* * θ *
o * * * o
S R
Since $\displaystyle RS = QR,\;\Delta QRS$ is isosceles.
. . Hence: .$\displaystyle \angle SQR \:=\:\angle QSR \:=\:\theta$
Since $\displaystyle QP \parallel RS,\;\angle PQS \:=\:\angle QSR \:=\:\theta$
Since $\displaystyle P$ can be anywhere to the upper-left on that line,
. . we cannot determine $\displaystyle \angle PSQ$
Nor can we find the lengths of $\displaystyle PQ$ and $\displaystyle PS$, or the area of $\displaystyle PQRS$.