Question

proving same side interior angles supplementary
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 1 cong angle 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:

Step1: Identify 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.

Step2: Identify the second blank

A linear pair of angles is supplementary by the Linear Pair Postulate.

Step3: Identify the third blank

Since \(\angle3\) and \(\angle1\) are supplementary (\(m\angle3 + m\angle1=180^{\circ}\)), this is based on the definition of supplementary angles (if two angles form a linear pair, their measures add up to \(180^{\circ}\)).

Answer:

1. Corresponding Angles Theorem
2. Linear Pair Postulate
3. definition of supplementary angles