Given:
[tex]m\angle ABC=46^\circ[/tex]
BD bisects angle ABC.
To find:
The [tex]m\angle ABD[/tex].
Solution:
It is given that, BD bisects angle ABC. It means, BD divides the angle ABC is two equal parts. So,
[tex]m\angle ABD=m\angle DBC=\dfrac{\angle ABC}{2}[/tex]
We need to find [tex]m\angle ABD[/tex], so
[tex]m\angle ABD=\dfrac{\angle ABC}{2}[/tex]
[tex]m\angle ABD=\dfrac{46^\circ}{2}[/tex]
[tex]m\angle ABD=23^\circ[/tex]
Therefore, the [tex]m\angle ABD[/tex] is 23°. Hence first option is correct.
