Final answer:
To find m∠ABC, we can use the angle bisector theorem and set up an equation using the given angles. By solving the equation, we find that m∠ABC is 50 degrees.
Step-by-step explanation:
To find m∠ABC, we need to use the angle bisector theorem, which states that a line that bisects an angle divides the opposite side into segments that are proportional to the adjacent sides of the angle.
Given m∠ABD = 5x and m∠DBC = 3x + 10, we can set up the equation:
5x = (3x + 10)
5x - 3x = 10
2x = 10
x = 5
Now we can substitute the value of x back into the given angles:
m∠ABD = 5(5) = 25 degrees
m∠DBC = 3(5) + 10 = 15 + 10 = 25 degrees
Since the angle bisector divides the angle into two congruent angles, m∠ABC = m∠ABD + m∠DBC = 25 + 25 = 50 degrees.