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Linear Pairs 873 Views


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Description:

Sure, Romeo and Juliet were a great pair, but they don't hold a candle to linear pairs. Find out more by clicking play.

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Transcript

00:05

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

00:11

Marshall-Mallow, Incorporated…

00:13

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

00:18

corporation has its advantages…

00:21

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

00:31

possible.

00:32

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

00:36

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

00:40

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

00:47

When Marshall goes to the gym for his first workout…

00:49

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

00:55

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

01:01

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

01:06

out how these two angles are related.

01:08

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

01:12

…Two supplementary adjacent angles formed by intersecting lines.

01:17

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

01:25

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

01:30

x and the other to equal four-fifths x.

01:34

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

01:40

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

01:46

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

01:50

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

02:15

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

02:20

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

02:23

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

02:27

four-fifths times x…

02:29

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

02:35

and see what's left over.

02:37

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

02:40

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

02:45

his front makes a 100-degree angle.

02:47

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

02:51

Feel the burn, Marshall!

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