The problem involves finding the measure of angle FDG. This is a geometry problem that appears to involve two intersecting lines, with expressions given for the angles involved.

To solve this, we need to use the fact that the sum of the angles formed by two intersecting lines is always 180 degrees. The angles at the intersection must satisfy this equation:

$\text{Angle CDF} + \text{Angle FDG} = 180^\circ$

From the image, angle CDF is represented by $x - 16$, and angle FDG is represented by $2x + 10$. Therefore, the equation is:

$(x - 16) + (2x + 10) = 180$

Now, solve for $x$:

$x - 16 + 2x + 10 = 180$ $3x - 6 = 180$ $3x = 186$ $x = 62$

Now substitute $x = 62$ into the expression for angle FDG:

$\text{Angle FDG} = 2(62) + 10 = 124 + 10 = 134^\circ$

So, the measure of angle FDG is 134 degrees.

Would you like further clarification or details?

Here are 5 related questions:

1. What is the general rule for the sum of angles formed by two intersecting lines?
2. How would the solution change if the angles were complementary instead of supplementary?
3. How do you solve for $x$ when working with angle expressions like this?
4. What are some real-world applications of angle relationships like this one?
5. How would you solve a similar problem if the angles were labeled differently?

Tip: When solving for unknown angles, always check if the angles are supplementary (adding up to 180°) or complementary (adding up to 90°), as this will guide the equations you use!