Question

jillong was tasked with identifying all the supplementary angles to ∠6 in the image below in a math assessment and the reason to support each statement. her response was as follows: m∠6 + m∠4 = 180 because they are corresponding angles. m∠5 + m∠6 = 180 because they are linear pairs. the diagram shows two parallel lines (that are cut by a transversal). image of two parallel lines cut by a transversal with angles labeled 1,2,3,4,5,6,7,8 is her response correct and complete? if not, please explain all her errors. her response is not fully correct, ∠6 and ∠4 are consecutive interior angles and ∠6 and ∠8 are also linear pairs. her response is not fully correct, she said corresponding instead of consecutive interior and she said linear pairs instead of adjacent interior angles. her response is correct. her response is not fully correct, she forgot ∠8 is a supplemental vertical angle to ∠6.

Explanation:

1. For \( m\angle6 + m\angle4 = 180^\circ \), \( \angle6 \) and \( \angle4 \) are consecutive interior angles (not corresponding angles) when two parallel lines are cut by a transversal, and consecutive interior angles are supplementary.
2. For \( m\angle5 + m\angle8 = 180^\circ \), \( \angle5 \) and \( \angle8 \) are not a linear pair. A linear pair is adjacent and supplementary, but here the relationship is different (and the correct reasoning should relate to angle relationships with parallel lines and transversal, and the error is misidentifying the angle pair as linear pair instead of the correct adjacent - interior - like or other correct angle - pair relationship in the context of parallel lines cut by transversal).

Answer:

Her response is not fully correct, she said corresponding instead of consecutive interior and she said linear pair instead of adjacent interior angles.