The following figures are not drawn to scale. Does each figure contain a pair of parallel lines? Give a brief reason for each answer.

Here are the solutions for each figure:

1.4.1
The two given angles are alternate interior angles.

$$125^\circ = 125^\circ$$

Since the alternate interior angles are equal, the lines are parallel.

• Answer: Yes
• Reason: Alternate interior angles are equal.

1.4.2
The two given angles are corresponding angles.

$$68^\circ = 68^\circ$$

Since the corresponding angles are equal, the lines are parallel.

• Answer: Yes
• Reason: Corresponding angles are equal.

1.4.3
The two given angles are consecutive interior angles (co-interior angles).

$$85^\circ + 95^\circ = 180^\circ$$

Since the consecutive interior angles sum to $180^\circ$, the lines are parallel.

• Answer: Yes
• Reason: Co-interior angles sum to $180^\circ$.

1.4.4
The two given angles are consecutive exterior angles.

$$43^\circ + 143^\circ = 186^\circ$$

Since the consecutive exterior angles do not sum to $180^\circ$, the lines are not parallel.

• Answer: No
• Reason: Co-exterior angles do not sum to $180^\circ$.