Question

1. based on the given angles below, are the lines e and f parallel? why or why not?
2. based on the given angles below, are the lines c and d parallel? why or why not?
3. based on the given angles below, are the lines c and d parallel? why or why not?
4. based on the given angles below, are the lines a and b parallel? why or why not?
5. based on the given angles below, are the lines y and z parallel? why or why not?
6. based on the given angles below, are the lines g and h parallel? why or why not?

Explanation:

Step1: Recall parallel - line angle rules

If corresponding angles are equal, alternate - interior angles are equal, or same - side interior angles are supplementary (sum to 180°), the lines are parallel.

Step2: Analyze question 7

The angles 65° and 60° are neither corresponding, alternate - interior, nor supplementary. So, lines E and F are not parallel.

Step3: Analyze question 8

The two 54° angles are corresponding angles. Since corresponding angles are equal, lines C and D are parallel.

Step4: Analyze question 9

The angles 128° and 49° are neither corresponding, alternate - interior, nor supplementary. So, lines C and D are not parallel.

Step5: Analyze question 10

The angles 62° and 50° are neither corresponding, alternate - interior, nor supplementary. So, lines A and B are not parallel.

Step6: Analyze question 11

The angles 123° and 120° are neither corresponding, alternate - interior, nor supplementary. So, lines Y and Z are not parallel.

Step7: Analyze question 12

The 53° and 127° angles are same - side interior angles and 53°+127° = 180°. Since same - side interior angles are supplementary, lines G and H are parallel.

Answer:

1. The lines E and F are not parallel because the given angles are neither corresponding, alternate - interior, nor supplementary.
2. The lines C and D are parallel because the corresponding angles are equal.
3. The lines C and D are not parallel because the given angles are neither corresponding, alternate - interior, nor supplementary.
4. The lines A and B are not parallel because the given angles are neither corresponding, alternate - interior, nor supplementary.
5. The lines Y and Z are not parallel because the given angles are neither corresponding, alternate - interior, nor supplementary.
6. The lines G and H are parallel because the same - side interior angles are supplementary.