Corresponding Angles Worksheets - Free Printable

To solve for the value of \( x \) in each figure, we will use the properties of corresponding angles and other angle relationships when two parallel lines are cut by a transversal. Let's go through each problem step by step.

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1)

[](https://i.imgur.com/1234567.png)

#### Solution:
- The given angles are \( 146^\circ \) and \( 34^\circ \).
- These angles are supplementary because they form a linear pair (they lie on a straight line).
- Therefore, their sum is \( 180^\circ \):
\[
146^\circ + 34^\circ = 180^\circ
\]
- The angle \( x \) is the same as the angle adjacent to \( 146^\circ \), which is \( 34^\circ \).

Thus, \( x = 34^\circ \).

---

2)

[](https://i.imgur.com/2345678.png)

#### Solution:
- The given angles are \( 93^\circ \) and \( 87^\circ \).
- These angles are vertical angles, which means they are equal.
- However, since they are not directly related to \( x \), we need to focus on the relationship between the angles formed by the transversal.
- The angle \( x \) is the corresponding angle to \( 93^\circ \) because the lines are parallel.
- Therefore, \( x = 93^\circ \).

Thus, \( x = 93^\circ \).

---

3)

[](https://i.imgur.com/3456789.png)

#### Solution:
- The given angles are \( 75^\circ \) and \( 105^\circ \).
- These angles are supplementary because they form a linear pair.
- The angle \( x \) is the alternate interior angle to \( 75^\circ \) because the lines are parallel.
- Therefore, \( x = 75^\circ \).

Thus, \( x = 75^\circ \).

---

4)

[](https://i.imgur.com/4567890.png)

#### Solution:
- The given angles are \( 60^\circ \) and \( 111^\circ \).
- The angle \( x \) is the exterior angle to the triangle formed by the transversal.
- Using the exterior angle theorem, the exterior angle is equal to the sum of the two non-adjacent interior angles:
\[
x = 60^\circ + 111^\circ = 171^\circ
\]

Thus, \( x = 171^\circ \).

---

5)

[](https://i.imgur.com/5678901.png)

#### Solution:
- The given angles are \( 150^\circ \) and \( 30^\circ \).
- The angle \( x \) is the alternate interior angle to \( 150^\circ \) because the lines are parallel.
- Therefore, \( x = 150^\circ \).

Thus, \( x = 150^\circ \).

---

6)

[](https://i.imgur.com/6789012.png)

#### Solution:
- The given angles are \( 53^\circ \) and \( 128^\circ \).
- The angle \( x \) is the corresponding angle to \( 53^\circ \) because the lines are parallel.
- Therefore, \( x = 53^\circ \).

Thus, \( x = 53^\circ \).

---

7)

[](https://i.imgur.com/7890123.png)

#### Solution:
- The given angles are \( 131^\circ \) and \( 49^\circ \).
- The angle \( x \) is the alternate interior angle to \( 131^\circ \) because the lines are parallel.
- Therefore, \( x = 131^\circ \).

Thus, \( x = 131^\circ \).

---

8)

[](https://i.imgur.com/8901234.png)

#### Solution:
- The given angles are \( 103^\circ \) and \( 17^\circ \).
- The angle \( x \) is the corresponding angle to \( 103^\circ \) because the lines are parallel.
- Therefore, \( x = 103^\circ \).

Thus, \( x = 103^\circ \).

---

9)

[](https://i.imgur.com/9012345.png)

#### Solution:
- The given angles are \( 114^\circ \) and \( 66^\circ \).
- The angle \( x \) is the alternate interior angle to \( 114^\circ \) because the lines are parallel.
- Therefore, \( x = 114^\circ \).

Thus, \( x = 114^\circ \).

---

Final Answers:

\[
\boxed{
\begin{array}{ccc}
1) & x = 34^\circ & \\
2) & x = 93^\circ & \\
3) & x = 75^\circ & \\
4) & x = 171^\circ & \\
5) & x = 150^\circ & \\
6) & x = 53^\circ & \\
7) & x = 131^\circ & \\
8) & x = 103^\circ & \\
9) & x = 114^\circ & \\
\end{array}
}
\]