Math Problem Statement

BD bisects angle ABC. Find the measure of ABD. Angle ABD= (3x-17) and Angle CBD = (7x-39)

Solution

Given that BDBD bisects ABC\angle ABC, the measures of ABD\angle ABD and CBD\angle CBD are equal.

So, we can set up the equation: ABD=CBD\angle ABD = \angle CBD

Given: ABD=3x17\angle ABD = 3x - 17 CBD=7x39\angle CBD = 7x - 39

Since BDBD bisects ABC\angle ABC, we equate the two expressions: 3x17=7x393x - 17 = 7x - 39

Now, solve for xx:

  1. Subtract 3x3x from both sides: 17=4x39-17 = 4x - 39

  2. Add 39 to both sides: 22=4x22 = 4x

  3. Divide both sides by 4: x=224=5.5x = \frac{22}{4} = 5.5

Now, substitute x=5.5x = 5.5 back into the expression for ABD\angle ABD:

ABD=3(5.5)17=16.517=0.5\angle ABD = 3(5.5) - 17 = 16.5 - 17 = -0.5

Given that this value is not physically meaningful for an angle, recheck the setup. If the expressions were correctly assigned, the procedure above would be valid. Consider that angles are usually positive in standard interpretation. Without specific contextual reasons, a negative angle might be an error in formulation.

Would you like to clarify any of these steps or understand an alternative approach? Here are some questions you might find useful:

  1. Could we re-evaluate the setup of the angle equations?
  2. Do you need further explanation on angle bisectors?
  3. Would you like to explore another similar problem?
  4. Could there be additional constraints on xx we haven't considered?
  5. Should we discuss potential negative angle interpretations?

Tip: When solving for angles, always check if the context implies positive values unless specified otherwise.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angle Bisectors
Equations

Formulas

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Theorems

Angle Bisector Theorem

Suitable Grade Level

Grades 9-10