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. By the Corresponding Angles Theorem, corresponding angles are congruent.
• For the second blank: A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays. By the Linear Pair Postulate, a linear pair of angles is supplementary.
• For the third blank: Since \(m\angle3 + m\angle1=180^{\circ}\) (from the linear pair relationship) and we are using the fact that we can substitute \(m\angle5\) for \(m\angle1\) (because \(m\angle1 = m\angle5\)), this is an application of the Substitution Property.

Answer:

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