Answer:
x = 3
Step-by-step explanation:
Notice that we have both angles are congruent. That means we can apply the Angle Bisector Theorem, which states that for a triangle whose angle is bisected, then a/c = b/d (see attachment).
Here, a = 32, c = 6x + 6, b = 24, and d = 9x - 9. Plug these into the formula:
a/c = b/d
32/(6x + 6) = 24/(9x - 9)
Cross-multiply:
24 * (6x + 6) = 32 * (9x - 9)
144x + 144 = 288x - 288
144x = 432
x = 3
Thus, x = 3.
