ShmoopTube

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Here's your shmoop du jour.

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Line FG is parallel to Line IJ. If Angle F =

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40°, and Angle I = 85°, what is the measure of Angle GHJ?

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And here are your potential answers...

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Alright, we're told that angle F = 40°,

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and angle I = 85°, and they want us to use that information to find the measure of GHJ.

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First we should try to find GHJ's supplementary

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angle, the one that'll form a straight angle and help it add up to 180 degrees... either

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angle IHJ or FHG will do. Let's find angle FHG, because... well, it's closer

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Since FG and IJ are parallel, angles I and G are alternate interior angles.

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In other words, they're on opposite-inside sides of the transversal, the line that cuts

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across two parallel lines. That means that they are congruent, or the

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same, and since I measures 85 degrees, that means G does too.

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We already know angle F, so now we just have to solve for the final angle in the triangle,

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which is angle FHG. To do that, we add angles F and G, and subtract that from 180 degrees.

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We get 55 degrees as our answer.

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That's only the supplementary angle, remember... our last step is to subtract 55 from 180.

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We get 125 degrees, which means that our answer is C.

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