Question

Line BD bisects angle ABC. Line ABC = 8x. Line ABD = 2x + 22. Find line DBC

Answer 1

Since BD bisects angle ABC,

∠ ABD = ∠ DBC

So, ∠ DBC = 2x + 22     (1)

Also, ∠ DBC = ∠ ABC - ∠ ABD.

= 8x - (2x + 22)

= 8x - 2x - 22

= 6x - 22     (2)

From (1) and (2),

2x + 22 = 6x - 22

2x - 6x = -22 - 22

- 4x = - 44

x = 11

∠ DBC =  2x + 22 = 2(11) + 22 = 44

Hence, ∠ DBC = 44°.