Question

In a parallelogram the angle bisectors of two adjacent angles intersect at angles.

• A. acute
• B. obtuse
• C. right

Answer 1

The correct option is C right

Let ABCD be a parallelogram.
Consider two adjacent angles $\angle A$ and $\angle B$
$\angle A+\angle B={180}^0$
[Adjacent angles of parallelogram are supplementary]
$\frac{\angle A}{2}+\frac{\angle B}{2}=\frac{{180}^0}{2}$
[Angular bisectors of $\angle A$ and $\angle B$]
$\frac{\angle A}{2}+\frac{\angle B}{2}={90}^0$
If these two angle bisectors meet, it forms a triangle and the sum of the measures of the angles,formed by the angle bisectors and commmon arm, is ${90}^0$.
$⟹$ The third angle where these angle bisectors meet will be ${90}^0$
[Since sum of all the angles of a triangle is ${180}^0$]