The image you provided contains a polygon with angles marked at various positions. To solve for $x$, we can apply the fact that the sum of interior angles of a polygon is related to its number of sides. Here’s the general formula for the sum of the interior angles of a polygon with $n$ sides:

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

Based on the image, it looks like we have a five-sided polygon. Let's calculate the sum of the interior angles for a five-sided polygon:

$\text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$

Now, we can sum up the given angles and set them equal to 540°. The given angles are:

• $121^\circ$
• $96^\circ$
• $162^\circ$
• $101^\circ$
• $x$ (the unknown angle)

So, the equation becomes:

$121^\circ + 96^\circ + 162^\circ + 101^\circ + x = 540^\circ$

Now, solve for $x$:

$480^\circ + x = 540^\circ$

$x = 540^\circ - 480^\circ = 60^\circ$

Therefore, the value of $x$ is $60^\circ$.

Would you like further details or clarification?

Here are some follow-up questions that might help you understand this concept better:

1. How do we calculate the sum of interior angles for polygons with more sides?
2. What is the formula for exterior angles of polygons?
3. What is the difference between interior and exterior angles in polygons?
4. How can you find an unknown angle in a triangle using the sum of angles?
5. What happens if you extend the number of sides of a polygon—how does that affect the sum of its interior angles?

Tip: Always double-check the number of sides in a polygon before calculating the sum of its interior angles!