are consecutive angles in a parallelogram supplementary(180 degrees) ? WILL GIVE MEDAL! please help!!

Question

mathstudent55 · Answer

Let's say you have 2 parallel lines, m and n, cut by transversal, t.
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wormynut · Answer

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mathstudent55 · Answer

Sorry, my computer just went nuts.

mathstudent55 · Answer

Angles 1 and 2 are same side interior angles.
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mathstudent55 · Answer

What is the relationship between angles 1 and 2?

mathstudent55 · Answer

Angle 3 is supplementary to angle 1.
We know by corresponding angles that angles 2 and 3 are congruent.
That means angle 2 is supplementary to angle 1.
This shows that when two parallel lines are cut by a transversal, same side interior angles are supplementary.

mathstudent55 · Answer

Now look at a parallelogram.
Each pair of consecutive interior angles is a pair of same side interior angles of two parallel lines cut by a transversal, so in any parallelogram, any two consecutive angles are supplementary.

wormynut · Answer

@mathstudent55 Got it! thanks!

mathstudent55 · Answer

You're welcome.