Mark (✓) against the correct answer:


Mark (✓) against the correct answer:

The bisectors of two adjacent angles of a parallelogram intersect at

(a) 30°

(b) 45°

(c) 60°

(d) 90°


(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.

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