Answer:
[tex]ABC = 130[/tex]
Step-by-step explanation:
Given
[tex]ABC=12x - 110[/tex]
[tex]ABD=3x+40[/tex]
[tex]DBC=2x - 10[/tex]
Required
Determine the measure of ABC --- Missing part of the question
First, we need to determine the value of x
Since, D is an interior of ABC, then
[tex]ABC = ABD + DBC[/tex]
[tex]12x - 110 = 3x + 40 + 2x - 10[/tex]
Collect Like Terms
[tex]12x - 3x - 2x = 110 + 40 - 10[/tex]
[tex]7x = 140[/tex]
Solve for x
[tex]x = 140/7[/tex]
[tex]x = 20[/tex]
Substitute 20 for x in [tex]ABC=12x - 110[/tex]
[tex]ABC = 12 * 20 - 110[/tex]
[tex]ABC = 240 - 110[/tex]
[tex]ABC = 130[/tex]
