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Hey everybody.
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We're going to take a look at this problem where we have a line with four rays sticking out of it and some angle information.
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And we are asked to figure out which rays are and aren't parallel.
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Okay? so this is our guiding question today.
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And the first thing we need to do whenever we look at a diagram like this is we need to fill in any angle information.
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Because at this point, i don't see anything that's necessarily corresponding or alternate interior.
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So i need to go ahead and do some investigation.
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So fill in angles.
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And to do this, we need to first think geometrically and then algebraically.
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So geometrically, we can say that let's call this angle x and let's call this angle y.
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So angles x and y geometrically we know that added together with the other angles they're next to they should add up to 180 degrees.
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So x and y will add to 180 degrees with their adjacent angles.
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And i love using the angle symbol because it's just so easy and faster, right? and you can totally do that.
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Okay? so now we're going to do some algebra.
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So this is geometry.
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Here's some algebra.
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I know that x plus 62 plus 58 equals 180.
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And i know that y plus 59 plus 61 also equals 180 degrees.
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So as you copy this down, as you're writing this down, i want you to take out your calculator.
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And begin calculating.
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So the first thing we're going to do on the left hand side is we are going to add 62 and 58.
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So we will get x plus, we're going to do 62 plus 58, which is 120 degrees equals 180...