Question

Lines l and m are intersected by transversal t, and l is parallel to m. Select all the angles that are supplementary to ∠1.

A. ∠3
B. ∠4
C. ∠5
D. ∠6
E. ∠7
F. ∠8

Answer 1

The angles that are supplementary to angle 1 when lines l and m are intersected by transversal t, and l is parallel to m, are angles 3, 5, and 8. These angles are either consecutive interior angles or alternate exterior angles to angle 1 on parallel lines.

Step-by-step explanation:

The question involves understanding angle relationships when a transversal intersects two parallel lines. To determine which angles are supplementary to ∠1 (angle 1), first recall that supplementary angles are two angles whose measures add up to 180 degrees. When parallel lines l and m are intersected by a transversal t, consecutive interior angles like ∠3 (angle 3) and ∠5 (angle 5), as well as alternate exterior angles like ∠7 (angle 7) and ∠8 (angle 8), are supplementary. Consequently, the angles supplementary to ∠1 are ∠3, ∠5, and ∠8.

1. ∠3 - Consecutive interior angle with ∠1 on parallel lines intersected by a transversal.
2. ∠5 - Consecutive interior angle on the other parallel line also intersected by the transversal.
3. ∠8 - Alternate exterior angle with ∠1 on parallel lines intersected by a transversal.

Options B (∠4), C (∠5), and F (∠8) are the correct choices.