Final answer:
Considering ∠BX bisects ∠ABC, which means ∠ABX = ∠CBX. By setting up and solving the equation 5x + 18 = 2(2x + 12), we obtain x = 6. Substituting x = 6 into m∠CBX gives us m∠ABX = m∠CBX = 24 degrees.
Step-by-step explanation:
Given that ∠BX bisects ∠ABC, it means ∠ABX = ∠CBX. If m∠ABC = 5x + 18 and m∠CBX = 2x + 12, we can set up the equation 5x + 18 = 2(2x + 12) because the bisected angles are equal.
By solving this equation, we first simplify it to 5x + 18 = 4x + 24. Subtract 4x from both sides to have x = 6.
Substitute the value of x = 6 into m∠CBX (which is the same as m∠ABX), we have m∠CBX = 2x + 12 = 2*6 + 12 = 24 degrees.
Therefore, the measure of angle ∠ABX is 24 degrees.
Learn more about Angle bisector theorem