Question

lines and m are intersected by transversal t. l m. which of the following angles are supplementary to ∠4? select all that apply. a. ∠5 b. ∠6 c. ∠7 d. ∠8

Explanation:

Step1: Recall supplementary - angle property

Two angles are supplementary if their sum is 180°. When two parallel lines \(l\) and \(m\) are cut by a transversal \(t\), we use angle - relationships.

Step2: Identify corresponding and linear - pair angles

\(\angle4\) and \(\angle5\) are same - side interior angles. Since \(l\parallel m\), \(\angle4+\angle5 = 180^{\circ}\) (same - side interior angles are supplementary).
\(\angle4\) and \(\angle6\) are not supplementary.
\(\angle4\) and \(\angle7\) are not supplementary.
\(\angle4\) and \(\angle8\) are same - side interior angles. Since \(l\parallel m\), \(\angle4+\angle8 = 180^{\circ}\) (same - side interior angles are supplementary).

Answer:

A. \(\angle5\), D. \(\angle8\)