Given:
Suppose point D is in the interior of ∠ABC
, m∠ABC=12x−110
, m∠ABD=3x+40
, and m∠DBC=2x−10.
To find:
The measure of ∠ABC.
Solution:
Since point D is in the interior of ∠ABC, therefore
[tex]m\angle ABC=m\angle ABD+m\angle DBC[/tex]
Substitute the given values, we get
[tex]12x-110=(3x+40)+(2x-10)[/tex]
[tex]12x-110=5x+30[/tex]
[tex]12x-5x=110+30[/tex]
[tex]7x=140[/tex]
Divide both sides by 7.
[tex]x=20[/tex]
The value of x is 20.
[tex]m\angle ABC=12x-110[/tex]
[tex]m\angle ABC=12(20)-110[/tex]
[tex]m\angle ABC=240-110[/tex]
[tex]m\angle ABC=130^\circ[/tex]
Therefore, the measure of ∠ABC is 130 degrees.
