Question

given: ( w parallel x ) and ( y ) is a transversal.
prove: ( angle 3 ) and ( angle 5 ) are supplementary.
use the drop - down menus to complete the proof.
given that ( w parallel x ) and ( y ) is a transversal, we know that ( angle 1congangle 5 ) by the
therefore, ( mangle 1 = mangle 5 ) by the definition of congruent. we also know that, by definition, ( angle 3 ) and ( angle 1 ) are a linear pair so they are supplementary by the
by the
( mangle 3 + mangle 1 = 180 ). now we can substitute ( mangle 5 ) for ( mangle 1 ) to get ( mangle 3 + mangle 5 = 180 ). therefore, by the definition of supplementary angles, ( angle 3 ) and ( angle 5 ) are supplementary.

Explanation:

• For the first blank: When two parallel lines \(w\parallel x\) are cut by a transversal \(y\), \(\angle1\) and \(\angle5\) are corresponding angles. Corresponding angles are congruent when the lines are parallel.
• For the second blank: A linear pair of angles (\(\angle3\) and \(\angle1\)) are supplementary by the linear - pair postulate.
• For the third blank: Since \(m\angle1 = m\angle5\) (from congruent angles) and \(m\angle3+m\angle1 = 180^{\circ}\) (from linear - pair postulate), we use the substitution property (if \(a = b\) and \(c + a=d\), then \(c + b=d\)).

Answer:

1. Corresponding Angles Theorem
2. Linear - Pair Postulate
3. Substitution Property