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(0) (2pts) Given 0 in the figure, sketch the angles3+0(6) (2 pts) Find the exaet vlues lor the coordlinalen af (he point W (Warning: 'This cirele is uot Mcirck...

Question

(0) (2pts) Given 0 in the figure, sketch the angles3+0(6) (2 pts) Find the exaet vlues lor the coordlinalen af (he point W (Warning: 'This cirele is uot Mcirck ) (Hint: Youl CILII eonstruct" riglc trInngk Tor which Wix "UMCN )IU'

(0) (2pts) Given 0 in the figure, sketch the angles 3+0 (6) (2 pts) Find the exaet vlues lor the coordlinalen af (he point W (Warning: 'This cirele is uot Mcirck ) (Hint: Youl CILII eonstruct" riglc trInngk Tor which Wix "UMCN ) IU'



Answers

In the figure below, $\triangle \mathrm{KOA} \cong \triangle \mathrm{AEK}$. Copy and complete the following equations for their equal parts. $$\angle 0=CANT\quad COPY\quad THE\quad FIGURE$$

Yeah. Oh I love these problems. At the end of the uh the assignment, they're usually a little more challenging and and uh rely a little more on your your previous knowledge. This one being no exception. It's a very popular type of problem that shows up on standardized tests. You know your state math tests or your S A T A C. T. Type test because it combines geometric and algebraic uh concepts and you have to have a solid understanding of both and able to uh in order to be able to uh solve it the problem when it's all said and done, we're simply being asked to find the measure of angle HBO. So our answer is going to be right here. Right? Well, it's gonna take a little while to get to that. Okay. We have to use the given statement that segments A. B and B. C. Or perpendicular. Okay. Of course. What that tells us is that that angle right? There is 90°.. Okay, so the angle A, B. O. And angle O. B. C. These two that are given right? We know those have to add up to 90. That's those two angles right there. Right So that's our first equation. And you'll notice that between the two expressions representing the angle measures we have both X and Y. And those expressions therefore we're not going to be able to solve it with a single equation. This is going to require us to use a system of equations to solve it. So again this is the type of problem very popular on standardized exams because of uh you know the combination of the two major concepts. So let's start with our first equation, angle angle HBO plus angle O. B. C. Past equal 90°.. Okay because we're giving those perpendicular segments therefore Angle HBO which is two x plus y plus angle O. B. C. Which is six X. Plus eight that asked to equal 90 again, all I did was substitute in the equivalent expression for those two ankles. Okay. Mhm. Now let's simplify that and we get eight X plus Y. Subtract the aid over to the other side equals 82. Don't worry about the degree symbol. We know that we're talking about angle measures here. So when it's all said and done we will answer our question with the degree symbol appropriately. No big deal. Okay. And now the next two statements were told that angle A. O. B. Is 23 Y plus 90. That's this angle right here, angle A. Or B. And angle bOC. That's the other angle right next to it. That's represented by four x Plus four. Well, notice that those two angles are supplementary. They are what we call a linear repair. Right adjacent supplementary angles. They form a straight line. So we know the son of those two angles has to be 180 angle A or B plus angle B. O. C. Has to equal 180 degrees supplementary. Well, replacing the angle with the appropriate algebraic expression, we get this. All right, let's simplify that. I'll put X first. So we have four X Plus 23 Y. And then you see 90 Plus four is 94 and we're gonna subtract that to the other side. So 1 80 -94. It was 86. And here folks, we have to fire if you've watched any of my other videos, you know, I like to use highlighters a lot I've learned during remote learning. You know, it's an easy way to emphasize points virtually because we can't see each other. So whoa, sorry, cancel that. Oh, that's what I wanted. All right. So these two equations here form our system, those two that you see highlighted in purple. Okay, so our geometry portion of the problem is done. We use our knowledge of perpendicular lines and complementary and supplementary angles to come up with the system of equations from here. It's algebra. So we're going to Stack The two Equations. We have eight x plus y equals 82 and we have four X plus 23 Y equals 86. Probably want to use the elimination method here. So I'm just gonna multiply the bottom equation by -2. And if you're wondering why negative to if you don't remember, it's because you want to get one of your variables to cancel out when you add the two equations together. So top equation stays the same bottom equation. We gotta multiply everything by negative two. So we got negative eight X. And -46 y. And I guess that's gonna be what negative 172. You see it's gonna work out beautifully. So now when we add the equations together, the X. Is canceled. And we're left with negative 45 y equals lovely enough negative 90. So dividing both sides by two. Okay, We get everybody negative 45 gives us why equals two. I said the answer instead of the process and now that we know what why is we can plug it in say right here. Yeah. And work out that equation for X. So eight X plus Y. Well, we know what why is why is too equals 82? Subtract the two and divide by eight And you get x equals 10. I know right? That's a good one. And now that we have those two answers, we can go all the way back to the top, remember X is 10 and why is too So we're going to be plugging those in right there. All right there. Remember in the end, that's what this problem is asking for the measure of angle fabio. So two times 10 plus two. So angle HBO is 22°.. Mhm. That was fun, yet challenging. Problem. And I hope you ah understood the explanation. Thanks for watching.

From the previous problem. We know that Angle R is equal to three X plus five degrees, and we know that X is equal to 13 substituting X in 13. In for acts, we have three times 13 plus five, which comes out to 44 degrees, so angle are

We want to know what angles have the Vertex at l So we have I'm sorry. Angles. We have angle. A l p. We have angle p l I and we have angle a l r. So there will be three different angles of Ella's a vertex.

Question number. Mhm. So, he hasn't given him diagram like this. That is the plan. I am. So this is a game plan. Oh yeah. Yeah. Mrs this is me. This is C. This is deep. It is given that A. B. Is perpendicular to. Indeed. All right. So this is Nigeria. It is given right. An angle a baby. Yeah. Anything thanks. Actually produced the baseball perpendicular. Also it is doing that the angle A BD As you want to buy three explosive critics. Okay. So it is given that anger Everybody in the country to buy three express 86 degrees. Okay. Uh they're doing that anger A. B. C. In the toronto To works manage 10. All right. So these are things like then then they're asking is we is perpendicular to and or not. Yeah. So maybe we're not gonna Yeah. Tonight. I see. Now I can see there and measurement of anger, You know, be difficult 90 days. Right. It was a very conservative retty You can write to buy to be ex perfectly. Six. Is it the continent being blind? What is anxiety 2 3 actually got a 90 minute statistics and we can talk to people by the X. Is equal to Testing for and by two There's a part of 51. Right? No accessible to everyone right now then what is one of the angle A. B. C. You can talk to works. I understand you can do to and talk to anyone understood As a counter under two miners then It is the Kyoto 92. Right? So clearly that measurement of angles A. B. C. is equal to 90 delivery to this not going to and being and mm hmm is not perpendicular to B. C. And Uh huh. It's not about whatever or two. Yeah. I didn't answer even line is but when the clock to the plane actually developed each line of defense. Thanks. That is not too so it is not what point of view. Thank you.


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