Question

MB and NB are bisectors of $\angle CBA$ and $\angle ABD$ respectively. Find the value of $\angle MBN$ (in degrees).

• A. 90

Answer 1

The correct option is A 90
$\text{MB bisects}\angle CBA\text{and NB bisects}\angle ABD.$

$\text{So,}\angle ABM=\frac{1}{2}\angle CBA\text{and}\angle ABN=\frac{1}{2}\angle ABD.$

$\text{Now,}\angle MBN=\angle ABM+\angle ABN\angle MBN=\frac{1}{2}\angle CBA+\frac{1}{2}\angle ABD\angle MBN=\frac{1}{2}(\angle CBA+\angle ABD)\angle MBN=\frac{1}{2}\angle CBD\angle MBN=\frac{1}{2}\times {180}^{\circ }\angle MBN={90}^{\circ }$

$\text{Therefore, the value of}\angle MBN\text{is}{90}^{\circ }.$