ShmoopTube

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Here’s your shmoop du jour, brought to you by parallel lines.

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Some are more delicious than others.

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ABCD is a parallelogram. If angle B is equal to 30°, what is the measure of angle ACB?

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Here are the potential answers...

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Okay, what do we know about parallelograms…?

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They look like rectangles that an elephant sat on…

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Well, we know that opposite sides are… parallel, obviously.

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We also know that opposite angles are congruent.

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So…because we’re told that angle B is 30 degrees…

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…we know that angle D is 30 degrees as well. Great.

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We’re dealing with a four-sided polygon, so we must have 360 total degrees.

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If 30 and 30…or 60…are already accounted for…

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…then the two remaining angles must make up the difference.

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So just subtract those 60 degrees from the 360 and we get 300…

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and once again we have opposite angles that must be equal.

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So…300 divided by 2 is 150.

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Line AC is bisecting that angle…leaving us with an angle of 75 degrees.

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Answer E.

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As in, “Elephant.”

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