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Find the values of $x$ and $y.$...

Question

Find the values of $x$ and $y.$

Find the values of $x$ and $y.$



Answers

Find the values of $x$ and $y.$

We know that X is 1 80 degrees causes the total measure minus 1 20 which gives us 60. So exit 60 and then we know that accident three y plus six are equivalent. In other words, we can set them equal to each other. And we just established that excess sixties and let them make love each other. So for why and we end up with y equals 18 cause three wise 54.

Hello. For this question, we need to calculate that the values of x and Y in this ray diagram or accept my measure, the certain angles. So to calculate two variables, we're going to need two different equations. And the first thing, um, that should be obvious is that X and why are part of the of the angle of this straight line here? So this angle here, which we know is 180 degrees. So if we know the value of this third chunk, we can right ex not plus, why not? Plus, um, some value that we don't know yet equals 180 degrees because this is a straight line. However, because these air intersecting lines, then the value of the angles is the same for the cells that are directly across. So because this angle is 50 degrees, this angle is also 50 degrees and the same thing For this side, this would have the same values x, and this would have the same value as why. But that's not important right now on the main thing is just that we know that this is true, that they all add up toe 180 degrees. Now we have one equation here and two unknowns, which we can't solve. We need to get another equation involving our variables. No, optimistically, we have a triangle here, and we know that the sum of the angles of a triangle are also 180 degrees. So it would be nice if we could get a different equation that involves one of our variables. We immediately know that 70 70 degrees, and why not? Are here. And now we just need to figure out this third angle to calculate Um What? Why not? Is explicitly So this is a if you remember from intersecting parallel lines, you mentally continue this line here. Here, You can think about this as two parallel lines with, um, one trans versatile with this trans versatile. And you know that this angle corresponds to this angle because they have the same position relative to the intersection. And because of that, we also know that this angle here is 50 degrees, so we can also write this. Now we have two different equations into unknowns, so we should hopefully be able to solve it. So, for the first equation, um, I'm gonna subtract over 70 and subtract over 50. So we're gonna have Why not equals 1 80 degrees? Um, Maya's 50 my 70. So 50 plus 70 is one. 20 so this would be wise 60 degrees. And now we can plug this value into original equation and calculate out what X is. So we can now write that. Why not? It's 60 degrees, and this gives us I'm gonna give myself a little more room here that acts not equals 180 degrees, minus 50 plus 60 is 110 degrees. So this gives us the X is 70 degrees and that's it.

We know that the measures of the angles are right. Triangles 180 degrees similar to all triangles cause all triangles add up to ah 180 degrees. Therefore, we can set all this equivalent to 1 80 Simplify. We know three X is equal to 42 degrees. Therefore set three x equal to 42 flow for axe excess 14 and why is nine

Hello. For this question, we need to use this ray diagram to calculate the values of X and Y, which are measuring angles here. Now, for a little bit of notation. The lions, with one red arrow on it, are parallel to the other line with one red arrow on it. And then the line with two red arrows on it is parallel to this line, which also has two red arrows on. Now we need to somehow get some algebraic equations from this geometric picture, and the best way to attack it is to know that the sum of the interior angles of a triangle are 180 degrees. We have two triangles, so we have two sets of angles that have to add up to 180 degrees, sir. So for the first triangle we have, why not plus 55 degrees plus something else. And for the second triangle, we have X plus 50 degrees, plus some other angle. Now it's a good thing that they told us these lines were parallel because that lets us relate angles from one figure to an angle on another. So because of this line is parallel here, and this line is parallel thes Two lines are parallel and you have a trans versatile. You know that this angle here is the same as this angle here. So that means that in our ex equation, we can write why here And similarly, we know that this angle here and this angle here are the same because these two lines are parallel to each other and they hit the same trans Mursal and they are corresponding angles, which is what allows youto say that, which means they have the same position relative to the intersection. It's kind of annoying to see when it's not fully drawn out here, but essentially we're using that. This angle is the same as this angle, whatever value it turns out today. So we know that this angle and this angle are the same. Which means that in our why equation, we have 50 decrees written here. So if we go through and actually calculate out what why is which I'm going to do down here? We have that one down here. We have that 180 degrees minus 50 degrees minus 55 degrees equals. Why not, um or why sorry. Keep saying why not? Um, which turns out to be 75 decrees. And once we have this, it's a simple matter to just plug this into this. A plug. Why back into this equation and calculate out what X is. I give myself a little bit more room. Here we have the X equals 180 minus 50 minus 75 which equals 55 degrees if you go through and calculated, and that's it.


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