Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Like

Report

No Related Subtopics

Johns Hopkins University

Missouri State University

Oregon State University

Utica College

00:05

Amrita B.

In Exercises $5-11$ you will have to visualize certain lines and planes not shown in the diagram of the box. When you name a plane, name it by using four points, no three of which are collinear. Write the postulate that assures you that $\overrightarrow{A C}$ exists.

00:34

Evan S.

Classify each statement as true or false. $S$ contains $\stackrel{\leftrightarrow}{A B}$.

00:27

Classify each statement as true or false. Plane $R$ intersects plane $S$ in $\stackrel{\leftrightarrow}{A B}$ .

01:05

Make a sketch showing four coplanar points such that three, but not four, of them are collinear.

Create your own quiz or take a quiz that has been automatically generated based on what you have been learning. Expose yourself to new questions and test your abilities with different levels of difficulty.

Create your own quiz

Yeah. Hi, guys. We're here to do some additional practice on finding the different angle on dark values, given a central inscribed or maybe even an angle, formed by intersecting chords and sequence. Really, This first example. Remember that angle X W D is an inscribed angle and inscribed angle is gonna be half of the arc that it sub tense, forcing our question mark to be 116 degrees. Because double the architect substance Question two. It's the reverse. If we have the Ark value, which is 1 78 then we know that the angle that sub tends, it is gonna be half that, so we know this is gonna be 89 degrees. Question three. This is the diameter automatically. This angle is 90 degrees by default. It's 90 degrees because it is a triangle inscribed in a semi circle. If over here is 1 80 it has to be. It's half the circle, half of that's 90. If this is 108 than half of that is going to be the opposite angle, which is going to be a total of 54 degrees. So this angle here in the corner is 54 degrees, leaving what's left from 90 since, well, these two angles have to equal 90 leaving an angle of 36 degrees. And that's what we want is a 30 60 year angle moving along to a couple. Other examples. Keep in mind like, let's say, question six, this is a great question. All right, here's what we know. We know that this ark is 1 40. That leaves the rest of the circle the rest of that major arc to be what's left out of 3 60. So that has a value of 220 degrees. Now, since this is an inscribed angle, the ark that it's sub tends is double it. So what's Double three X plus 23. Six X plus 46. So the value of this is six x plus 46. The value of this is nine x minus six, and the total sum of both of those arcs is 220. So we're gonna do is take six X plus 46 plus nine X minus six, and we're gonna set that equal 22 20. Well, it's going to get us 15 X plus 40 equals to 20 when we subtract 40 from 2 20 we get 1 80. So you're left with 15 X equals 1 80 then 1 80 divided by 15 equals 12. So now if we want to find any of our angles, I can plug a 12 into here. If I like, that's gonna be 36 plus 23. And now this angle here has a value of 53 degrees. Pardon me, 59 degrees. So you could You have to get clever here. And you gotta maybe piecing things together or use what you know, to figure some other information out. And then you might have worked backwards a little bit before. You can work for words, but, you know, they're just really good examples of how you use your different rules. Okay, I love questions. Seven, take a look at this one, because this arc here is sub tended by this angle, but also by this angle that's gonna force 10 X plus eight thio equal 12 X minus two. And then we could go and say All right, this is 10 equals two X. In other words, five equals X and then everyone to find the measure of y Z, which is this arc length right here. Let's first take five. Plug it into here. It gets us 58 but double that since this is an inscribed angle. So you're going to get 116 degrees for the Arcand question? So now we're combining some algebra and several of the themes that we know. Okay, now let's talk about some of the themes that we looked at in a previous video. Take a look at this. We have a tangent line here and an angle formed from that segment and the point of concurrency. Remember that this arc here is going to be double this angle. So we got 116 degrees is arc Q P. Which means if you take that away from 3. 60 this ark yeah, has a value of 2 44 so I can go ahead and say, All right, that's equal to 2 44. Or, in other words, 60 X equals to 40. Or, in other words, X equals four, and then we can proceed to solve for whatever else we needed. Right now, the goal was to find X. But there you go. So notice we're using the special rule for a angle that's formed by a tangent line in a secret. Okay, remember these rules here where we have an angle formed by two secret lines and the angles the exterior. Well, remember, in this situation, this angle is half of the difference between these two works. So here's what I know. Three X plus 12 is equal to a half of 45 plus 12 X plus three. Okay, well, that's three X plus 12 equals half of 45 is 22.5. And actually, let's make our lives a little easier. I'm gonna combine this first. And so let me erase this 45 and three make 48. So we're gonna have one half. Okay. 48 plus 12 x, which is gonna be 24 plus six x. Okay. And now I know that I get negative. Three X equals 12 and X equals negative four. Okay. And that would be your answer. So I know that the answer it seems odd that it's negative with the process is the important part. This angle switch colors. This angle here is half. Oh, you know what? Here's our issue. It's not half the sum. I meant to call this half the difference. Let's get rid of this. That needs to be a subtraction site. This is very, very different. This is to be a subtraction sign. So therefore, this should be a subtraction sign and this should be a subtraction sign. So therefore, let's clean this up a little bit. We're going to get three X plus 12 equals 24 minus six. So this makes a big difference. This gets us nine X equals 12, and therefore X equals 12 nights or, in other words, four thirds. So that would get us this angle here to be 16 when you plug in four thirds. And so therefore, we could also figure out this angle. Okay, four thirds of 16 is 12, 16, 16 plus three. So you get a 19 year okay, Awesome. And we have this one as well. Keep in mind that since we have two chords and an angle in question, that eight X plus 15 is half the sum of the two angles that its substance do U minus 10. There you go ahead and read this again. So we know eight x plus 15 equals half of some of 50 plus 15 x minus 10. That's half of 40 plus 15 x, which would equal 20 plus 7.5 X. All right, So if we were, that would get us a 0.5 X equals five. That's gonna get us X equals 10. And then if you want to find the measure of RS, we could just plug 10 into here. That's 150 minus 10. Or in other words, 140. So this is how you could use these themes and practice. You could do them all numerically. You have some algebra involved, but essentially we used our central inscribed. And then our angle therms from tangents and intersecting chords inside and outside of the circle. See you next time.

Parallel and Perpendicular lines

Deductive Reasoning

Non Rigid Transformations (Dilations)

Polygons

Geometry Basics

02:20

05:58

06:55

03:09