To determine the measure of angle $x$ in the given figure, let's follow the steps to solve the problem.

Step 1: Recall the sum of interior angles of a polygon.

For any $n$-sided polygon, the sum of all interior angles is given by:

$\text{Sum of interior angles} = (n - 2) \times 180^\circ$

Here, the polygon has 7 sides (heptagon). Thus:

$\text{Sum of interior angles} = (7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ$

Step 2: Add the known angles.

From the figure, the given interior angles are:

$128^\circ, \, 124^\circ, \, 133^\circ, \, 128^\circ, \, 117^\circ, \, 127^\circ$

Let’s add them together:

$128 + 124 + 133 + 128 + 117 + 127 = 757^\circ$

Step 3: Solve for angle $x$.

Since the total sum of angles in the heptagon is $900^\circ$, we can find $x$ by subtracting the sum of the known angles from $900^\circ$:

$x = 900^\circ - 757^\circ = 143^\circ$

Final Answer:

The measure of angle $x$ is:

$\boxed{143^\circ}$

Do you need further clarification on this solution or a step explained in more detail?
Here are 5 related questions to expand your understanding:

1. How is the formula for the sum of interior angles $(n-2) \times 180^\circ$ derived?
2. What are the properties of regular and irregular polygons regarding angles?
3. How would you calculate the sum of exterior angles of a polygon?
4. If a polygon has 8 sides, what is the sum of its interior angles?
5. How do interior angles relate to exterior angles in a polygon?

Tip: Always check that you have accounted for all the angles in a problem, as missing even one value can lead to incorrect results!