Question

if ( mangle7 + mangle8 = 180^circ ), which of the following can be concluded?
options:

• ( r ) is parallel to ( s ) by converse of alternate interior angles thm.
• ( v perp r ) by converse of alternate exterior angles thm
• ( s perp u ) by converse of alternate interior angles thm
• ( r ) is parallel to ( s ) by converse of consecutive interior angles thm

Explanation:

The Consecutive Interior Angles Theorem (also known as the Same - Side Interior Angles Theorem) states that if two lines are cut by a transversal and the consecutive interior angles are supplementary (their sum is \(180^{\circ}\)), then the two lines are parallel. Here, we are given that \(m\angle7 + m\angle8=180^{\circ}\), which means \(\angle7\) and \(\angle8\) are consecutive interior angles formed when a transversal cuts lines \(r\) and \(s\). By the Converse of the Consecutive Interior Angles Theorem, we can conclude that \(r\) is parallel to \(s\).

Answer:

r is parallel to s by Converse of Consecutive Interior Angles Thm.