Alternate Angles in Parallel Lines Worksheets - Free Printable
Educational worksheet: Alternate Angles in Parallel Lines Worksheets. Download and print for classroom or home learning activities.
PNG
405×574
16.5 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #843581
⭐
Show Answer Key & Explanations
Step-by-step solution for: Alternate Angles in Parallel Lines Worksheets
▼
Show Answer Key & Explanations
Step-by-step solution for: Alternate Angles in Parallel Lines Worksheets
To solve for the value of \( x \) in each figure, we will use the properties of alternate angles formed when two parallel lines are cut by a transversal. Here are the key properties:
1. Alternate Interior Angles: These are equal.
2. Alternate Exterior Angles: These are equal.
3. Corresponding Angles: These are equal.
4. Consecutive Interior Angles (Same-Side Interior Angles): These are supplementary (sum to 180°).
Let's solve each problem step by step.
---
- The given angles are \( 146^\circ \) and \( 68^\circ \).
- The angle \( x \) is an alternate interior angle to \( 68^\circ \).
- Therefore, \( x = 68^\circ \).
Answer: \( x = 68^\circ \)
---
- The given angles are \( 131^\circ \) and \( 49^\circ \).
- The angle \( x \) is an alternate exterior angle to \( 49^\circ \).
- Therefore, \( x = 49^\circ \).
Answer: \( x = 49^\circ \)
---
- The given angles are \( 123^\circ \) and \( 53^\circ \).
- The angle \( x \) is an alternate interior angle to \( 53^\circ \).
- Therefore, \( x = 53^\circ \).
Answer: \( x = 53^\circ \)
---
- The given angles are \( 62^\circ \) and \( 118^\circ \).
- The angle \( x \) is an alternate interior angle to \( 62^\circ \).
- Therefore, \( x = 62^\circ \).
Answer: \( x = 62^\circ \)
---
- The given angles are \( 125^\circ \) and \( 55^\circ \).
- The angle \( x \) is an alternate interior angle to \( 55^\circ \).
- Therefore, \( x = 55^\circ \).
Answer: \( x = 55^\circ \)
---
- The given angles are \( 102^\circ \) and \( 78^\circ \).
- The angle \( x \) is an alternate exterior angle to \( 78^\circ \).
- Therefore, \( x = 78^\circ \).
Answer: \( x = 78^\circ \)
---
- The given angles are \( 151^\circ \) and \( 29^\circ \).
- The angle \( x \) is an alternate interior angle to \( 29^\circ \).
- Therefore, \( x = 29^\circ \).
Answer: \( x = 29^\circ \)
---
- The given angles are \( 83^\circ \) and \( 97^\circ \).
- The angle \( x \) is an alternate interior angle to \( 97^\circ \).
- Therefore, \( x = 97^\circ \).
Answer: \( x = 97^\circ \)
---
- The given angles are \( 130^\circ \) and \( 50^\circ \).
- The angle \( x \) is an alternate interior angle to \( 50^\circ \).
- Therefore, \( x = 50^\circ \).
Answer: \( x = 50^\circ \)
---
\[
\boxed{
\begin{array}{ccc}
1) & x = 68^\circ & \\
2) & x = 49^\circ & \\
3) & x = 53^\circ & \\
4) & x = 62^\circ & \\
5) & x = 55^\circ & \\
6) & x = 78^\circ & \\
7) & x = 29^\circ & \\
8) & x = 97^\circ & \\
9) & x = 50^\circ & \\
\end{array}
}
\]
1. Alternate Interior Angles: These are equal.
2. Alternate Exterior Angles: These are equal.
3. Corresponding Angles: These are equal.
4. Consecutive Interior Angles (Same-Side Interior Angles): These are supplementary (sum to 180°).
Let's solve each problem step by step.
---
Problem 1
- The given angles are \( 146^\circ \) and \( 68^\circ \).
- The angle \( x \) is an alternate interior angle to \( 68^\circ \).
- Therefore, \( x = 68^\circ \).
Answer: \( x = 68^\circ \)
---
Problem 2
- The given angles are \( 131^\circ \) and \( 49^\circ \).
- The angle \( x \) is an alternate exterior angle to \( 49^\circ \).
- Therefore, \( x = 49^\circ \).
Answer: \( x = 49^\circ \)
---
Problem 3
- The given angles are \( 123^\circ \) and \( 53^\circ \).
- The angle \( x \) is an alternate interior angle to \( 53^\circ \).
- Therefore, \( x = 53^\circ \).
Answer: \( x = 53^\circ \)
---
Problem 4
- The given angles are \( 62^\circ \) and \( 118^\circ \).
- The angle \( x \) is an alternate interior angle to \( 62^\circ \).
- Therefore, \( x = 62^\circ \).
Answer: \( x = 62^\circ \)
---
Problem 5
- The given angles are \( 125^\circ \) and \( 55^\circ \).
- The angle \( x \) is an alternate interior angle to \( 55^\circ \).
- Therefore, \( x = 55^\circ \).
Answer: \( x = 55^\circ \)
---
Problem 6
- The given angles are \( 102^\circ \) and \( 78^\circ \).
- The angle \( x \) is an alternate exterior angle to \( 78^\circ \).
- Therefore, \( x = 78^\circ \).
Answer: \( x = 78^\circ \)
---
Problem 7
- The given angles are \( 151^\circ \) and \( 29^\circ \).
- The angle \( x \) is an alternate interior angle to \( 29^\circ \).
- Therefore, \( x = 29^\circ \).
Answer: \( x = 29^\circ \)
---
Problem 8
- The given angles are \( 83^\circ \) and \( 97^\circ \).
- The angle \( x \) is an alternate interior angle to \( 97^\circ \).
- Therefore, \( x = 97^\circ \).
Answer: \( x = 97^\circ \)
---
Problem 9
- The given angles are \( 130^\circ \) and \( 50^\circ \).
- The angle \( x \) is an alternate interior angle to \( 50^\circ \).
- Therefore, \( x = 50^\circ \).
Answer: \( x = 50^\circ \)
---
Final Answers
\[
\boxed{
\begin{array}{ccc}
1) & x = 68^\circ & \\
2) & x = 49^\circ & \\
3) & x = 53^\circ & \\
4) & x = 62^\circ & \\
5) & x = 55^\circ & \\
6) & x = 78^\circ & \\
7) & x = 29^\circ & \\
8) & x = 97^\circ & \\
9) & x = 50^\circ & \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of angles in parallel lines worksheet.
