Question

Please help I’ve tried this many times but can’t get it

Answer 1

x = 3

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.