Need of the answer to this question (geometry)

The line TR is being split right down the middle by the line QS. The line QS is being split right down the middle by TR. Doesn't this then mean that the two half sections on both sides of either line are equal? For example, 3x should equal 12 because TR is being split down the middle by QS. By the same logic, 8 should equal 2x because Qs is being split down the middle by TR.

3x = 12



x = 4

Likewise,

2x = 8



x = 4

In both cases, x = 4. It can even be plugged in to the problem itself and the solutions will be true.