Question

What is the angle formed between the angle bisectors of any two adjacent angles of a parallelogram?

• A. 90°
• B. 45°
• C. 75°
• D. 105°

Answer 1

The correct option is A 90°

Let the parallelogram be PQRS as shown and bisectors QO and RO bisects angle Q and angle R respectively.We know that adjacent angles of a parallelogram are supplementary.
$\therefore \angle PQR+\angle QRS=180°$

Since, QO and RO are angle bisectors,
$\therefore \frac{\angle PQR}{2}+\frac{\angle QRS}{2}=\frac{180°}{2}$
$or,\angle ORQ+\angle OQR=90°$

$\therefore$In triangle OQR
$\angle ROQ=180°-(\angle ORQ+\angle OQR)$
$\Rightarrow ROQ=180°-90°=90°$