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 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 expand the parentheses:

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

We'll combine the X terms:

$0.38x+176.2=180$

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

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

$0.38x=3.8$

We'll divide both sides by 0.38:

$x=10$