https://file.aiquickdraw.com/mathbot/file/1726774338897dx8jy8cx.jpg

Examine the diagram above and determine the following:

The angle relationship is

The value of x is equal to

The measure of the missing angle is

The given diagram shows two intersecting lines, forming a pair of vertically opposite angles. Let's analyze the relationships and solve for \(x\).

### 1. **Angle Relationship:**
The two angles shown in the diagram, 155° and \(x - 13\), are **vertically opposite angles**. Vertically opposite angles are always equal when two lines intersect.

Therefore, we can set up the equation:
\[
x - 13 = 155°
\]

### 2. **Solve for \(x\):**
To find the value of \(x\), solve the equation:
\[
x - 13 = 155
\]
Add 13 to both sides:
\[
x = 155 + 13
\]
\[
x = 168
\]

### 3. **Measure of the Missing Angle:**
The missing angle is \(x - 13\), which is the expression given in the diagram.

Since we've solved \(x = 168\), substitute this value back into the expression:
\[
x - 13 = 168 - 13 = 155°
\]

Thus, the missing angle is \(155^\circ\).

---

In summary:
- **Angle Relationship:** Vertically opposite angles.
- **Value of \(x\):** \(x = 168^\circ\).
- **Measure of the missing angle:** \(155^\circ\).

Would you like further clarification, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. What are the properties of vertically opposite angles?
2. How do corresponding angles compare to vertically opposite angles in intersecting lines?
3. If the angle next to 155° were given, how could you use supplementary angles to find it?
4. How would the solution change if the angle opposite to \(x - 13\) was not 155° but a different value?
5. Can you find an example where vertically opposite angles are used in real-world designs?

**Tip:** Vertically opposite angles are always equal, no matter the angle size, due to the symmetry of intersecting lines.

Examine the diagram above and determine the following: The angle relationship is, The value of x is equal to, The measure of the missing angle is

Solve a geometry problem involving two intersecting lines. Determine the relationship between vertically opposite angles, solve for x in the equation x - 13 = 155, and calculate the missing angle. Suitable for students in Grades 8-10.

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