Answer:
(b.) Angles 6 and 8 are supplementary
(c.) Angle 1 is congruent to Angle 4
(d.) Angle 2 is congruent to Angle 7
Explanation:
Explaining b. Angles 6 and 8 are supplementary:
- When two lines are parallel and cut by a traversal, the same side interior angle and its accompanying same side exterior angle are supplementary.
There are four pairs of these supplementary angles in this diagram including:
- Angles 2 and 4,
- Angles 6 and 8,
- Angles 1 and 3,
- and Angles 5 and 7.
Explaining c. Angle 1 is congruent to Angle 4:
- When two lines are parallel and cut by a traversal, vertical angles are made, which are always congruent.
- These are the angles opposite each other when two lines cross.
There are also four sets of vertical angles in the diagram including:
- Angles 1 and 4,
- Angles 2 and 3,
- Angles 5 and 8,
- and Angles 6 and 7.
Explaining d. Angle is congruent to Angle 7:
- When two lines are parallel and cut by a traversal, alternate exterior angles are made.
- Alternate exterior angles always lie outside two lines that are cut by the transversal and they are located on the opposite sides of the transversal.
- Thus, the two exterior angles which form at the alternate ends of the transversals in the exterior part are considered as the pair of alternate exterior angles and they are always congruent.
There are two pairs of alternate exterior angles in the diagram:
- Angles 1 and 8,
- and Angles 2 and 7.