ShmoopTube

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

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They cut more lines than film editors.

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Line j is parallel to line k.

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What is the measure of angle z in terms of x and y?

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And here are the potential answers...

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All righty…well, the first thing that jumps out at us is that there isn’t

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a single number to be seen in the diagram provided.

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It’s a good thing, then, that this problem asks for us to find z in terms of x and y…

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The problem makes a big deal out of the fact that j and k are parallel…

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So… why should we care that j and k are parallel?

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Well, because they’re parallel, we know that the corresponding angles

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created by a transversal are congruent.

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That would be those two light saber-y lines that are creating our three angles.

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In other words, because THIS angle is y degrees, then THIS angle must also be y degrees.

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Same thing with our friend angle x over here.

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So now, we’ve got three angles all on one side of a straight line.

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A straight line, we know, creates an angle of 180 degrees…

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…so angle z must be equal to 180 minus the measure of the other two angles combined.

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Or… z = 180 – (x + y) Answer A.

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