Consider the below figure attached with the question.
Given:
m∠DBC = (12x - 3), m∠DBE = (5x + 12), m∠EBC = (3x + 13).
To find:
The measure of ∠EBC.
Solution:
From the figure, it is clear that,
[tex]m\angle DBC-m\angle DBE=m\angle EBC[/tex]
Putting the given values, we get
[tex](12x-3)-(5x+12)=(3x+13)[/tex]
[tex]12x-3-5x-12=3x+13[/tex]
[tex]7x-15=3x+13[/tex]
[tex]7x-3x=15+13[/tex]
[tex]4x=28[/tex]
Divide both sides by 4.
[tex]x=7[/tex]
Now,
[tex]m\angle EBC=(3x+13)^\circ[/tex]
[tex]m\angle EBC=(3(7)+13)^\circ[/tex]
[tex]m\angle EBC=(21+13)^\circ[/tex]
[tex]m\angle EBC=34^\circ[/tex]
Therefore, the measure of angle EBC is 34 degrees.
