Angles on the same side of a transversal and also inside the lines the intersects.

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Same side inner angles space two angle that are on the very same side the the transversal and also on the internal of (between) the 2 lines.

Figure \(\PageIndex1\)

Same Side inner Angles Theorem: If two parallel present are cut by a transversal, then the exact same side inner angles space supplementary.

Figure \(\PageIndex2\)

If \(l \parallel m\), then \(m\angle 1+m\angle 2=180^\circ\).

Converse the the same Side interior Angles Theorem: If two lines are cut by a transversal and also the very same side interior angles are supplementary, climate the lines space parallel.



Example \(\PageIndex2\)

Give two instances of exact same side interior angles in the diagram:

Figure \(\PageIndex5\)


There are countless examples of same side inner angles in the diagram. Two room \(\angle 6\) and \(\angle 10\), and also \(\angle 8\) and \(\angle 12\).

Example \(\PageIndex3\)

Find the worth of \(x\).

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\(y\) is a very same side internal angle v the significant right angle. This method that \(90^\circ+y=180\) therefore \(y=90\).

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