https://file.aiquickdraw.com/mathbot/file/17261147961195m7rw11q.jpg

Let's go through the questions in the image to solve for the missing angles based on the given angles, using the properties of angles formed by parallel lines and transversals:

### Concepts to Use:
1. **Supplementary Angles**: Angles on a straight line add up to 180°.
2. **Vertical Angles**: Opposite angles formed by two intersecting lines are equal.
3. **Alternate Interior Angles**: If a transversal crosses parallel lines, alternate interior angles are equal.

### Solutions:

1. **Question 1**: 
   - The angle given is 101°.
   - The missing angle forms a linear pair with it, so:  
     \[
     180° - 101° = 79°
     \]

2. **Question 2**:
   - Given one angle is 80°. The missing angle is its vertical angle, which is also 80° (Vertical angles are equal).

3. **Question 3**:
   - The angle given is 122°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 122° = 58°
     \]

4. **Question 4**:
   - The angle given is 53°.
   - The missing angle is the vertical angle of 53°, so it’s also 53°.

5. **Question 5**:
   - The angle given is 114°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 114° = 66°
     \]

6. **Question 6**:
   - The angle given is 89°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 89° = 91°
     \]

7. **Question 7**:
   - The angle given is 100°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 100° = 80°
     \]

8. **Question 8**:
   - The angle given is 131°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 131° = 49°
     \]

9. **Question 9**:
   - The angle given is 105°.
   - The missing angle is the vertical angle of 105°, so it’s also 105°.

10. **Question 10**:
   - The angle given is 82°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 82° = 98°
     \]

11. **Question 11**:
   - The angle given is 103°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 103° = 77°
     \]

12. **Question 12**:
   - The angle given is 50°.
   - The missing angle forms a linear pair with it, so:
     \[
     180° - 50° = 130°
     \]

---

Would you like a detailed explanation for any of the questions or concepts?

### 5 Follow-up Questions:
1. What are alternate exterior angles, and how are they used in angle calculations with parallel lines?
2. How can we prove that vertical angles are equal?
3. What is the difference between corresponding and alternate interior angles?
4. Can we determine the missing angle if both angles on the parallel lines are unknown?
5. How do consecutive interior angles relate to each other on parallel lines?

### Tip:
When dealing with angles on parallel lines, always look for linear pairs and vertical angles first, as they provide straightforward calculations.

Find the measure of each angle indicated on parallel lines given the existing angles.

Solve for the missing angles in a parallel lines problem using linear pairs, vertical angles, and alternate interior angles. This example covers key geometry concepts and theorems suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation