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Given that Line m is parallel to line n.
We  prove that 1 is supplementary to 3 as follows:

[tex]\begin{tabular} {|c|c|} Statement&Reason\\[1ex] Line m is parallel to line n&Given\\ \angle1\cong\angle2&Corresponding angles\\ m\angle1=m\angle2&Deifinition of Congruent angles\\ \angle2\ and\ \angle3\ form\ a\ linear\ pair&Adjacent angles on a straight line\\ \angle2\ is\ supplementary\ to\ \angle3&Deifinition of linear pair\\ m\angle2+m\angle3=180^o&Deifinition of supplementary \angle s\\ m\angle1+m\angle3=180^o&Substitution Property \end{tabular}[/tex]
[tex]\begin{tabular} {|c|c|} \angle1\ is\ supplementary\ to\ \angle3&Deifinition of supplementary \angle s \end{tabular}[/tex]

Two angles whose sum is 180° are called supplementary angles. The table of the proof that ∠1 is supplementary to ∠3 can be filled as shown below.

What are supplementary angles?

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The given table can be completed as shown below, for the proof that ∠1 is supplementary to ∠3.

  1. Line m in is parallel to line n  →  Given
  2. ∠1 = ∠2  →  Corresponding angles
  3. m∠1 = m∠2  →  Deifinition of Congruent angles
  4. ∠2 and ∠3 for a linear pair  →  Adjacent angles on a straight line
  5. ∠2 is supplementary to ∠3  →  Definition of linear pair
  6. m∠2 + m∠3 = 180°  →  Definition of supplementary angles
  7. m∠1 + m∠3 = 180°  →  Substitution Property
  8. ∠1 is supplimentary to ∠3

Hence, the table of the proof that ∠1 is supplementary to ∠3 can be filled as shown above.

Learn more about Supplementary Angles:

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