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°

Answer 1

(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:
$$\begin{gathered} \frac{A}{2}\mathrm{and}\frac{B}{2}\mathrm{or}\frac{A}{2}=(90-\frac{A}{2}) \\ \mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{is}180°. \\ \frac{\angle A}{2}+90-\frac{\angle A}{2}+\angle O={180}^{\circ } \\ \angle O=180-90 \\ \angle O={90}^{\circ } \end{gathered}$$

Hence, the two bisectors intersect at right angles.