https://r2.erweima.ai/mathbot/image/1726069659720as3d5r1w.jpg

The image shows two intersecting lines, forming vertically opposite angles. One angle is labeled \( 105^\circ \), and the opposite angle is labeled \( x + 10^\circ \).

Since vertically opposite angles are always equal, we can set up the equation:

\[
x + 10 = 105
\]

To solve for \( x \), subtract 10 from both sides:

\[
x = 105 - 10 = 95
\]

Thus, the value of \( x \) is \( 95 \).

Would you like more details or have any questions? Here are some related questions to further your understanding:

1. What are the properties of vertically opposite angles?
2. How would the equation change if the other angle were \( 2x + 5 \) instead of \( x + 10 \)?
3. How can you solve for \( x \) if angles form a straight line instead of being vertically opposite?
4. Can vertically opposite angles ever be supplementary?
5. What are the angle properties in different types of triangles?

**Tip**: Always check the diagram carefully to identify angle relationships like vertical or supplementary angles.

What is the value of x? Write only a number.

Solve for x using vertically opposite angles. In this example, one angle is labeled as 105° and the other as x + 10°. Use basic algebra to find the value of x.

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