Question

$ABCD$ is the parallelogram. $P$, $Q$, $R$ and $S$ are the mid points of sides $AB$, $BC$, $CD$ and $AD$. If $\angle A={70}^o$. Find the acute angle of intersection of diagonal of parallelogram $PQRS$.

• A. ${110}^o$
• B. ${60}^o$
• C. ${70}^o$
• D. ${65}^o$

Answer 1

The correct option is C ${70}^o$

Here as $S$ and $Q$ are mid points so $AB||SQ$ or $AP||SO$.
similarly,
$AS||PO$
So, $APOS$ is parallelogram
So, $\angle A=\angle SOP\text{(opposite angles of ||gm)}$
So, $\angle SOP={70}^o$
which is the acute angle of intersection of diagonals of parallelogram $PQRS$.

Hence, correct option is $\left(c\right)$.