Answer:
C. 21°
Step-by-step explanation:
In triangle ABC, perpendiculars dropped on the sides AB and AC from the ray BD are equal in measure or congruent.
Therefore, ray BD is equidistant from the sides AB and AC.
So, ray BD will be the bisector of angle ABC.
[tex] \therefore m\angle ABD = m\angle DBC[/tex]
(Angle bisector theorem)
[tex] \therefore (3x+9)\degree = (45-6x)\degree [/tex]
[tex] \therefore 3x+9 = 45-6x[/tex]
[tex] \therefore 3x+6x = 45-9[/tex]
[tex] \therefore 9x = 36[/tex]
[tex] \therefore x =\frac{36}{9}[/tex]
[tex] \therefore x =4[/tex]
[tex] \therefore (3x+9)\degree = (3*4+9)\degree=(12+9)\degree =21\degree [/tex]
[tex] \implies m\angle ABD=21\degree [/tex]
