Explanation:
Since DE is a midsegment, it divides the side AB into two congruent segments. Therefore, we can conclude that angle ADE is congruent to angle BDE. Using this fact and the given angle measures, we can set up an equation and solve for x:
ADE = BDE (since DE is a midsegment)
3x + 7 = 5x - 2 (substitute the given angle measures)
7 = 2x - 2 (subtract 3x from both sides)
9 = 2x (add 2 to both sides)
x = 4.5
Therefore, the solution is x = 4.5.