Question:
Mark (✓) against the correct answer:
The bisectors of two adjacent angles of a parallelogram intersect at
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Solution:
(d) 90°
We know that the opposite sides and the angles in a parallelogram are equal.
Also, its adjacent sides are supplementary, i.e. sum of the sides is equal to 180.
Now, the bisectors of these angles form a triangle, whose two angles are:
$\frac{A}{2}$ and $\frac{B}{2}$ or $\frac{A}{2}=\left(90-\frac{A}{2}\right)$
$\frac{\angle A}{2}+90-\frac{\angle A}{2}+\angle O=180^{\circ}$
$\angle O=180-90$
$\angle O=90^{\circ}$
Hence, the two bisectors intersect at right angles.