Solve for X: Triangle Angle Equation (120.2-X = 0.88X+50)

Let's remember that the sum of angles in a triangle equals 180 degrees.

Therefore, to find $x$, we will use the following equation:

$A+B+C=180$

Now let's substitute in the known data:

$\frac{1}{2}x+6+120.2-x+0.88x+50=180$

We'll factor out $x$ as a common term in the equation:

$x(\frac{1}{2}-1+0.88)+176.2=180$

Let's next expand the parentheses:

$\frac{1}{2}x-x+0.88x+176.2=180$

Then, we'll combine the $x$ terms:

$0.38x+176.2=180$

Now we'll move terms to opposite sides and maintain the appropriate sign:

$\text{0}.38x=180-176.2$

$0.38x=3.8$

Finally, we will divide both sides by 0.38 to get our answer:

$x=10$