Question

m∠6 + m∠7 = 180°
a) y || z: alternate interior angles converse
b) y || z: converse of corresponding angles thm.
c) w || x: alternate interior angles converse
d) w || x: consecutive interior angles converse

Explanation:

Step1: Identify Angle Relationship

∠6 and ∠7 are consecutive interior angles (they lie between two lines and on the same side of a transversal). The given equation is \( m\angle6 + m\angle7 = 180^\circ \), meaning they are supplementary.

Step2: Apply Converse Theorem

The Consecutive Interior Angles Converse states that if two consecutive interior angles are supplementary, then the two lines cut by the transversal are parallel. Here, the lines are \( w \) and \( x \), cut by the transversal forming ∠6 and ∠7. So this theorem applies to \( w \parallel x \).

Step3: Match with Options

Option D states \( w \parallel x \): Consecutive Interior Angles Converse, which matches our analysis.

Answer:

D) \( w \parallel x \): Consecutive Interior Angles Converse