Answer
m$\angle$ABC = 98$^{\circ}$
Work Step by Step
Since ray BD bisect $\angle$ABC:
m$\angle$ABD = m$\angle$DBC
Substitute the values from the problem...
2x + 15 = 3x - 2
Subtract 2x from both sides.
2x - 2x + 15 = 3x - 2x - 2
15 = x - 2
Add 2 to both sides.
15 + 2 = x - 2 + 2
17 = x
Substitute the value of x into either of the smaller angles.
m$\angle$ABD = 2x + 15
m$\angle$ABD = 2(17) + 15
m$\angle$ABD = 49$^{\circ}$
Since both smaller angles are congruent...
m$\angle$ABC = 2(m$\angle$ABD)
m$\angle$ABC = 2(49)
m$\angle$ABC - 98$^{\circ}$
