Answer:
Angle 1: 145 degrees
Angle 2: 35 degrees
Angle 3: 145 degrees
Angle 4: 35 degrees
Angle 5: 145 degrees
Angle 6: 35 degrees
Angle 7: 145 degrees
Angle 8: 35 degrees
Explanation:
1) See above.
2) Angles 4 and 2 are equal, because they are vertical angles (share a vertex) where two parallel lines are cut by a transversal (line c?)
Angles 1 and 2 equal 180 degrees when added together, so 180 - 35 = 145, which is the measure of angle 1.
Angles 1 and 3 are also vertical, and therefore equal.
When two or more lines are cut by a transversal, the angles that are in the same relative position are corresponding angles.
When the lines are parallel, the corresponding angles are congruent.
Congruent angles are equal. So Angle 1 = Angle 5 and Angle 2 = Angle 6. Then the rules for vertical angles apply again, giving you the measures for angles 7 and 8.
3) 1 and 3 are vertical, 2 and 4 are vertical, 5 and 7 are vertical, 6 and 8 are vertical.
1 and 5 are corresponding, 2 and 6 are corresponding, 3 and 7 are corresponding, 4 and 8 are corresponding.
4) 1 and 2, 3 and 4, 5 and 6, 7 and 8 are all supplementary pairs.
1 and 4, 2 and 3, 5 and 8, and 6 and 7 are supplementary pairs.
1 and 3, 2 and 4, 5 and 7, 6 and 8 are equal pairs because they are vertical.
1 and 5, 2 and 6, 3 and 7, 4 and 8 are equal pairs because they are corresponding.
Hopefully this covers all they wanted.