Final answer:
To find the measure of ∆ABC when BD bisects it, add the expressions given for m∆ABD and m∆DBC to form an equation representing m∆ABC. Combine like terms to simplify the equation. The exact measurement of ∆ABC can be calculated if the value of x is known.
Step-by-step explanation:
To find the measure of ∆ABC when BD bisects ∆ABC, we use the given expressions for m∆ABD=(3x+26) and m∆DBC=(8x−34). Since BD is the bisector, we know that m∆ABD and m∆DBC add up to m∆ABC. Therefore, we can set up the equation:
(3x + 26) + (8x - 34) = m∆ABC
Combining like terms we get:
11x - 8 = m∆ABC
We don't have the exact value of x, but this equation represents the relationship between x and m∆ABC. If x were known, we could find the exact measurement of ∆ABC by solving for m∆ABC.