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∠BX bisects ∠ABC. If m∠ABC = 5x + 18 and m∠CBX = 2x + 12, find the m∠ABX. [Draw, mark up, and label a diagram!]

User Phyxx
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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

User Uliysess
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