It appears that the image contains two similar triangles. To solve for the unknown value $x$, we can use the property of similar triangles, which states that the corresponding sides of similar triangles are proportional.

From the image:

• The first triangle has side lengths 60 (OP) and 20 (PQ).
• The second triangle has corresponding side lengths 180 (RS) and $x$ (QS).

To set up a proportion: $\frac{OP}{RS} = \frac{PQ}{QS}$ Substituting the known values: $\frac{60}{180} = \frac{20}{x}$ Simplifying the left side: $\frac{1}{3} = \frac{20}{x}$ Now, solve for $x$ by cross-multiplying: $1 \cdot x = 3 \cdot 20$ $x = 60$

Thus, the unknown measurement $x$ is 60.

Would you like further details or clarifications on this? Here's some additional related questions:

1. How do we know that the triangles are similar in the first place?
2. What other properties of similar triangles can help in solving problems like this one?
3. Can we apply this same method to three-dimensional figures?
4. How do we use the Pythagorean theorem in similar triangles?
5. What happens if the triangles are not proportional but just have equal angles?

Tip: Always make sure to carefully verify if the triangles in the problem are indeed similar by checking corresponding angles or sides.