Question

The angle between the bisectors of two adjacent supplementary angles is

• A. acute angle
• B. right angle
• C. obtuse angle
• D. none of these

Answer 1

The correct option is B right angle

Consider two supplementary angles,

$\angle OBA+\angle OBC=180$
such that, $MB$ bisects $\angle OBA$ and $NB$ bisects $\angle OBC$

$\angle OBA+\angle OBC=180$

$\frac{1}{2}(\angle OBA+\angle OBC)=90$

$\angle MBO+\angle NBO=90$

$\angle MBN={90}^{\circ }$
Thus, bisectors of two adjacent angles form a right angle between them.