Question

1. determine if the following lines are parallel.

Explanation:

Step1: Recall parallel - line criteria

If corresponding angles are equal, or alternate - interior angles are equal, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze the first pair of lines

The two angles marked as \(105^{\circ}\) are corresponding angles. Since corresponding angles are equal (\(105^{\circ}=105^{\circ}\)), the lines \(l\) and \(m\) are parallel.

Step3: Analyze the second pair of lines

There is no information about the angles formed by the transversal with lines \(l\) and \(m\) to determine if they are parallel. So, we cannot say if they are parallel or not.

Step4: Analyze the third pair of lines

There is no information about the angles formed by the transversal with lines \(l\) and \(m\) to determine if they are parallel. So, we cannot say if they are parallel or not.

Step5: Analyze the fourth pair of lines

The angles \(125^{\circ}\) and \(65^{\circ}\) are same - side interior angles. Since \(125^{\circ}+65^{\circ}=190^{\circ}
eq180^{\circ}\), the lines \(l\) and \(m\) are not parallel.

Answer:

1. Yes/No: Yes, Justification: Corresponding angles are equal.
2. Yes/No: Cannot be determined, Justification: Insufficient angle information.
3. Yes/No: Cannot be determined, Justification: Insufficient angle information.
4. Yes/No: No, Justification: Same - side interior angles are not supplementary.