ShmoopTube

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Here’s your shmoop du jour, brought to you by supplementary angles.

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It must be that lotion they’ve been using that makes them so supple…mentary.

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Find the sum of angles N and O in terms of n.

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Here are the potential answers...

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Okay, so we’ve got this poor triangle, which is apparently being dragged along by a string…

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All righty, so… we want to know the sum of the angles N and O…

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in terms of angle…little n.

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The “sum” part is important.

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What that tells us is that we don’t need to figure out what N and O are individually…

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…just what they equal, in relation to angle little n…together.

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Well, the first thing we can figure out is the measure of angle M.

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Since it’s adjacent to angle little n, and the two angles exist along a straight line…

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…they are referred to as supplementary…

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…meaning they total 180 degrees.

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We also know that the three angles inside the triangle must total 180 degrees…

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…so we can deduce that N and O combined… must make up the difference.

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If M = 180 minus little n…

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…and the sum of N and O equal 180 minus M…

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…then we can plug the value for M into our new equation, and cancel out the 180’s…

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…to find that angles N and O are equal to the measure of angle little n.

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Boom…it's answer A.

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Uh oh… the Triangle Humane Society just called. Better run, kid…

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