The diagram you've uploaded shows two intersecting lines, which form a pair of vertically opposite angles. The two angles are labeled as:

• $x + 119$ (on the left)
• $79 + x$ (on the right)

Because these angles are vertically opposite, they are equal. This gives us the equation:

$x + 119 = 79 + x$

Now, let's solve for $x$:

1. Subtract $x$ from both sides:

$119 = 79$

This is a contradiction. The equation seems to indicate that both angles on the left and right are actually the same based on a geometric fact (vertical angles should be equal), but their values do not align.

There might be a mistake in the angle values provided, since solving this gives an impossible result. Could you check if the given angle measures are correct?

Let me know if you'd like to clarify or check another approach.

Now, for further practice and deeper understanding:

1. What are vertically opposite angles?
2. How do corresponding angles relate to parallel lines?
3. How do you solve for unknowns in geometric diagrams?
4. What is the sum of angles on a straight line?
5. How does altering one equation term affect both sides of the equation?

Tip: Always check if an equation derived from a diagram makes logical sense, especially in geometric problems!