Find measure of vertical angles (video) | Khan Academy

Video transcript

So we have two intersecting lines here, and then we have this early purple-looking lineage. And then they’ve given us some angles. They tell us that the bill of this fish right over here is 7x. The standard of this slant veracious over here is 60 degrees. And the measure of this angle right over hera is x. So permit ‘s try to figure out what all of these angles are. so to do that, we have to figure out what ten is. And there ‘s a boastfully clue here, because the 60-degree angle plus the x slant, they ‘re adjacent. And if you add these two angles together, their outer rays, our upright angle with this 7x angle. So we could say — and equitable to visualize that a little better, let me color it in. actually, let me do it this way. You see that this angle out here — let me do it in a color I have n’t used yet. This integral fish over here, which is going to be 60 degrees plus adam, that ‘s a vertical slant with this angle, the one that has measure 7x. So we could say that 60 degrees plus x is equal to 7x because upright angles are equal. So get ‘s write that down. We get 60. And we ‘ll assume that everything is in degrees. 60 plus — let me do that in this other coloring material. 60 plus x is going to be equal to 7x. And nowadays we barely have to solve for ten. So the simplest thing to do would be to get all over x ‘s on one side of the equation. I ‘ve already gotten seven x ‘s on this right-hand side, so lease ‘s get rid of all of the x ‘s on the left-hand side. And the easiest way to get rid of this ten is to subtract adam from the left-hand side. But of course, in arrange to keep it an equation, we ca n’t precisely do something to one slope. differently, it won’t be equal anymore. We have to do it to both sides. So get ‘s subtract x from both sides. And on the left side, we are left with just the 60. So we ‘re left with precisely a 60. And then that is going to be equal to 7x minus adam. If I have 7 of something and I get rid of 1 of them, I ‘m going to have 6 of that something left. So that ‘s going to be equal to 6x. So we have 6 times something is equal to 60. You could credibly figure that out in your head. But I will do it a short systematically. We can divide both sides by 6 to solve for x. So let ‘s do that. And we would be left with x is adequate to. 60 divided by 6 is 10. And we reminded ourselves that everything was in degrees. And we could even do that here. This was in degrees. This is in degrees. And so this is in degrees right over here. So the meter of this angle right over here is 10 degrees. so this one right over there is 10 degrees. This is, of run, 60 degrees. You add them in concert, 60 degrees plus 10 degrees is 70 degrees. so this bigger slant right over here is 70 degrees. And of course, this one over here, it ‘s a vertical slant. It ‘s going to have to be the like. And we see that, 7 times ten. 7 times 10 degrees is 70 degrees adenine well.

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