Practice problems for finding the value of x in vertical angles.

To solve the problems involving vertical angles, we need to use the property that vertical angles are congruent. This means that when two lines intersect, the angles opposite each other (called vertical angles) are equal.

Let's go through each problem step by step:

---

Problem 1:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 50^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 50^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 50^\circ
\]

#### Answer:
\[
\boxed{50}
\]

---

Problem 2:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 75^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 75^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 75^\circ
\]

#### Answer:
\[
\boxed{75}
\]

---

Problem 3:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 120^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 120^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 120^\circ
\]

#### Answer:
\[
\boxed{120}
\]

---

Problem 4:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 85^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 85^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 85^\circ
\]

#### Answer:
\[
\boxed{85}
\]

---

Problem 5:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 60^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 60^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 60^\circ
\]

#### Answer:
\[
\boxed{60}
\]

---

Problem 6:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 90^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 90^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 90^\circ
\]

#### Answer:
\[
\boxed{90}
\]

---

Problem 7:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 110^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 110^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 110^\circ
\]

#### Answer:
\[
\boxed{110}
\]

---

Problem 8:

[Image description: Two intersecting lines forming four angles. One angle is labeled as \( x \), and its vertical angle is labeled as \( 45^\circ \).]

#### Solution:
- The angle labeled \( x \) is a vertical angle to the angle labeled \( 45^\circ \).
- Since vertical angles are congruent, we have:
\[
x = 45^\circ
\]

#### Answer:
\[
\boxed{45}
\]

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Final Answers:

\[
\boxed{50, 75, 120, 85, 60, 90, 110, 45}
\]