Question

nina and rob were arguing about parallel lines cut by transversal questions. the diagram shows two parallel lines cut by a transversal. alice said that was wrong and you need at least 2 angles to find all the angles. who is correct? is either correct? explain.

alice is correct because with 2 angles you can fill in the supplemental vertical, corresponding, and alternate interior/exterior angles and the congruent linear pairs and consecutive interior fill in the rest.

alice is correct. you must have at least 2 angles because you won’t be able to find the other supplemental angles without it.

rob is correct. if you have one angle, you can fill in the supplemental vertical, corresponding, and alternate interior/exterior angles and the congruent linear pairs and consecutive interior fill in the rest.

rob is correct. if you have one angle, you can fill in the congruent vertical, corresponding, and alternate interior/exterior angles and the supplemental linear pairs and consecutive interior fill in the rest.

Explanation:

When dealing with parallel lines cut by a transversal, if we know one angle, we can use properties like vertical angles (congruent), corresponding angles (congruent), alternate interior/exterior angles (congruent), and linear pairs (supplementary) along with consecutive interior angles (supplementary) to find all other angles. So knowing one angle is sufficient, which supports Rob's statement.

Answer:

Rob is correct. If you have one angle, you can fill in the congruent vertical, corresponding, and alternate interior/exterior angles and the supplementary linear pairs and consecutive interior fill in the rest.