ShmoopTube

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Linear Pairs, a la Shmoop. Marshall E. Mallow has spent decades building

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Marshall-Mallow, Incorporated…

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…a multi-million-dollar marshmallow empire. Being the president of a wealthy marshmallow

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corporation has its advantages…

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Fancy cruises, private jets, swanky banquets, and more s'mores than you'd think was humanly

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possible.

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Of course, it has its downsides, too… Marshall knows that if he wants to rule the

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marshmallow market for another 25 to 30 years, he'll need to take better care of himself.

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So he hires a personal trainer who can whip him into shape.

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When Marshall goes to the gym for his first workout…

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…the personal trainer tells him to do sit-ups so that his back makes an angle with the floor…

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…that is four-fifths times the measure of the angle his front side makes with the floor.

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What are the measures of these angles? Before we do anything else, we should figure

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out how these two angles are related.

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Well, it shouldn't be too hard to tell that these two angles are linear pairs…

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…Two supplementary adjacent angles formed by intersecting lines.

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Since linear pairs are supplementary, their measures add up to 180 degrees.

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Since one angle is four-fifths the measure of the other, we can set one angle to equal

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x and the other to equal four-fifths x.

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And because we know the two angles add up to 180 degrees, we can set up the equation

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"x plus four-fifths x equals 180" and solve for x.

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Adding the two x terms together gives us nine-fifths x equals 180.

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If we multiply both sides by five ninths, we'll get our answer: x equals 100.

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That's the measure of one of the angles: 100 degrees. But what about the other?

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We have two ways to find the measure of the other angle.

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We can either multiply 100 by four-fifths because we know that the remaining angle is

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four-fifths times x…

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…or, since the two angles have to add up to 180 degrees, we can subtract 180 by 100

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and see what's left over.

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In both cases, we should get 80 degrees as the other angle.

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Mr. Mallow has to do sit-ups so that his back makes an 80-degree angle with the floor and

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his front makes a 100-degree angle.

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No sweat! Well, maybe a little sweat for Marshall E. Mallow.

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Feel the burn, Marshall!

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