Answer:
Angle ABD = 45 degrees
Angle DBC = 45 degrees
Step-by-step explanation:
If the ray BD bisects ABC, then it divides it in two angles of equal measure. The we can write the following equality:
angle ABD = Angle DBC
9 x + 9 = 12 x - 3
solve for x by subtracting 9x from both sides,
9 = 3 x - 3
and adding 3 to both sides:
9 + 3 = 3 x
12 = 3 x
divide both side by 3 to isolate "x":
12/3 = x
x = 4
And now we can find the value of each angle:
Angle ABD = 9 x + 9 = 9 (4) + 9 = 36 + 9 = 45 degrees
Angle DBC = 12 x - 3 = 12 (4) - 3 = 18 - 3 = 45 degrees
