Answer:
141°
Step-by-step explanation:
If BD is an angle ABC bisector, then by angle bisector definition,
[tex]m\angle ABD=m\angle DBC[/tex]
Given
[tex]m\angle ABD=10x-17\\ \\m\angle DBC=6x+18[/tex]
Therefore,
[tex]10x-17=6x+18\\ \\10x-6x=18+17\\ \\4x=35\\ \\x=\dfrac{35}{4}=8.75[/tex]
Now, find the measure of the whole angle ABC:
[tex]m\angle ABC=2m\angle ABD=2(10x-17)^{\circ}=(20x-34)^{\circ}=\\ \\=(20\cdot 8.75-34)^{\circ}=141^{\circ}[/tex]
