Question

In the diagram, bisects ABC. Find mABD and mDBC

Answer 1

Angle ABD = 45 degrees

Angle DBC = 45 degrees

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