ShmoopTube

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Here’s your shmoop du jour, brought to you by an insane number of angles.

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Seriously…these angles should be locked up in an institution.

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Lines l and m are parallel, and lines j and k are parallel.

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If angle 1 is 130°, how many angles are equal to 60°?

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Here are the potential answers...

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Wowsers. What a madcap, dizzying patchwork of lines and angles we have to deal with here.

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So this problem is really just testing what we know about angles and transversals.

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When we have a couple of parallel lines, and we slice through ‘em with another line…

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we create a bunch of similar angles every which way.

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In other words, which angles equal which other angles when a transversal comes along and cuts things up?

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Well, let’s start with the angles directly adjacent to angle 1.

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We’re told this angle is 130 degrees…which means that both of the angles right next to

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it must be 50 degrees each… since they exist along a straight line.

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We know the angle across from it – angle 3 – is also 130 degrees… either because

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we get this result by subtracting the other three angles from 360.

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It looks like ALL of our angles here are going to be either 130 or 50 degrees…

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…which leaves room for absolutely zero of them to have a measure of 60 degrees.

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That was a trick question. So, the answer is A.

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