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Linear Pairs 874 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.
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
Full Transcript
- 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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