Final answer:
To prove the measure of m∠ABD, we use the given angle relationships and solve for x, finding it to be 14, which corresponds to a m∠ABD measure of 59 degrees.
Step-by-step explanation:
To solve the problem, we need to understand that angle measures in a geometric figure must add up according to known theorems or postulates. In this case, we are given two expressions for the measures of two angles, m∠ABD and m∠DBC, and the actual measure of their sum, m∠ABC (140°). Therefore, m∠ABD + ∠DBC = ∠ABC. We set up the equation (3x + 17) + (5x + 11) = 140 and solve for x. After simplification, we have 8x = 112, which gives us x = 14. Returning to the given expression for m∠ABD, we calculate it as 3(14) + 17 = 59 degrees, proving the required angle measure.