Can someone please walk me through this step by step?

Subhotosh Khan said:
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this assignment.
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Actually, I don’t know how to do this at all. I’m just learning this math for fun to get ahead of my grade. (7th). What I have tried to do is join D to C. I know then that angle D is 20 degrees and angle C is the same as angle B. But I cannot really figure anything else out, so I’m asking for help in how to do these problems.
 
The Velociraptors said:
Actually, I don’t know how to do this at all. I’m just learning this math for fun to get ahead of my grade. (7th). What I have tried to do is join D to C. I know then that angle D is 20 degrees and angle C is the same as angle B. But I cannot really figure anything else out, so I’m asking for help in how to do these problems.
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The angles you are referring to would be equal IF AB || CD, but they are not.
 
The Velociraptors said:
Actually, I don’t know how to do this at all. I’m just learning this math for fun to get ahead of my grade. (7th). What I have tried to do is join D to C. I know then that angle D is 20 degrees and angle C is the same as angle B. But I cannot really figure anything else out, so I’m asking for help in how to do these problems.
Click to expand...
Can you see how the 76 degree arc relates to a couple of the angles? Did you look up the theorems that apply to this kind of figure (inscribed angles and arcs)?

Or do you know the theorem referred to in post #4? Either way can lead to the answer.
 
Dr.Peterson said:
Can you see how the 76 degree arc relates to a couple of the angles? Did you look up the theorems that apply to this kind of figure (inscribed angles and arcs)?

Or do you know the theorem referred to in post #4? Either way can lead to the answer.
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Well, according to #4, 76 degrees can be used to find angle x by splitting arc BC into 1/2 and adding it to arc AD which is 76 degrees. I know about the inscribed angle theorem, but I’m just now realizing that it’s applicable to this question. Is it because BC is the arc ”subtended” by the 20 degree angle? Just wondering why half of arc BC has to be added to half of arc AD to find angle x. So, following #4, angle x is 20 degrees + 76 degrees?
 
pka said:
In the figure let point at \(X\) so the theorem is \(m\angle (BXC)=\frac{1}{2}m\widehat{BC}+m\widehat{AD}\) AND We already know be the inscribed angle theorem \(m\widehat{BC}=40^o\).
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The Velociraptors said:
Well, according to #4, 76 degrees can be used to find angle x by splitting arc BC into 1/2 and adding it to arc AD which is 76 degrees. I know about the inscribed angle theorem, but I’m just now realizing that it’s applicable to this question. Is it because BC is the arc ”subtended” by the 20 degree angle? Just wondering why half of arc BC has to be added to half of arc AD to find angle x. So, following #4, angle x is 20 degrees + 76 degrees?
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\(\frac{1}{2}(76+40)=58\) therefore \(m(\angle BXC)=58^o\)
To: Velociraptors, why are you trying to do or why have you been assigned problems about which you seemingly know nothing about the theory upon which the problems are based.
 
pka said:
\(\frac{1}{2}(76+40)=58\) therefore \(m(\angle BXC)=58^o\)
To: Velociraptors, why are you trying to do or why have you been assigned problems about which you seemingly know nothing about the theory upon which the problems are based.
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I was never assigned these things. I’m a seventh grader who is trying to teach myself new things, and I’m simply learning. It’s not wrong to want to know new things is it? I have memorized the theories, but I’m new to applying them, so I’m practicing. Sorry to bother you guys.
 
The Velociraptors said:
I was never assigned these things. I’m a seventh grader who is trying to teach myself new things, and I’m simply learning.
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Ah! Thank you for explaining it. But that means that you completely have misunderstood the nature and purpose of this site. We are a HELP site. That means we try to help you do problems. You need someone to help guide you in learning the material in the first place. Here is a very good elementary geometry text College Geometry by Musser&Trimpe.
 
The Velociraptors said:
I was never assigned these things. I’m a seventh grader who is trying to teach myself new things, and I’m simply learning. It’s not wrong to want to know new things is it? I have memorized the theories, but I’m new to applying them, so I’m practicing. Sorry to bother you guys.
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It's great to be studying on your own, and to realize that you don't have to be taught by someone else. A good textbook and a willingness to try things is all it takes (with an occasional help from others).

It's also good to know that you have seen (at least some of) the theorems, which I asked about. (It would help if you told us which theorems you know.) Now we have to work on applying them. (I think you're doing better than pka suggested; but your saying "I don’t know how to do this at all" gave the wrong impression.)

The Velociraptors said:
Well, according to #4, 76 degrees can be used to find angle x by splitting arc BC into 1/2 and adding it to arc AD which is 76 degrees. I know about the inscribed angle theorem, but I’m just now realizing that it’s applicable to this question. Is it because BC is the arc ”subtended” by the 20 degree angle? Just wondering why half of arc BC has to be added to half of arc AD to find angle x. So, following #4, angle x is 20 degrees + 76 degrees?
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As I said, there are a couple different ways you can use the theorems for this.

You've observed that the 20 degree angle at A tells you that arc BC is 40 degrees, and then you can use the theorem pka talked about to find x = (40 + 76)/2 = 116/2 = 58 degrees, though you wrote that wrong.

It sounds like you haven't seen that theorem, though. That, and others, can be found here (among many other places): https://mathbitsnotebook.com/Geometry/Circles/CRAngles.html

Which of the theorems do you know? pka's is #4.

Now, here's the other way I had in mind: The inscribed angle theorem applied to arc AD tells us that angle B is 76/2 = 38 degrees. Then, looking at triangle ABX (taking point X to be the vertex of angle x), we have two interior angles, whose sum will be the other exterior angle. Have you learned about that? That makes x = 20 + 38 = 58 degrees. (This is one way to prove the other theorem.)

Again, we'll be happy to work with you as you study on your own. The more you tell us about what you've learned and show what you've tried, the more easily we can communicate with you and understand what help you need.
 
pka said:
Ah! Thank you for explaining it. But that means that you completely have misunderstood the nature and purpose of this site. We are a HELP site. That means we try to help you do problems. You need someone to help guide you in learning the material in the first place. Here is a very good elementary geometry text College Geometry by Musser&Trimpe.
Click to expand...
That means I have misunderstood the purpose of this site partly. I did not realize it would not give me step by step guidance; however, I did post problems and showed what steps I have taken to solve. I have read the rules. Anyway, thank you for suggesting this book, and I will purchase it, though I‘m wondering if it’s available PDF. Then I will post questions in correspondence to what I have learned. Thank you again.
 
Dr.Peterson said:
It's great to be studying on your own, and to realize that you don't have to be taught by someone else. A good textbook and a willingness to try things is all it takes (with an occasional help from others).

It's also good to know that you have seen (at least some of) the theorems, which I asked about. (It would help if you told us which theorems you know.) Now we have to work on applying them. (I think you're doing better than pka suggested; but your saying "I don’t know how to do this at all" gave the wrong impression.)


As I said, there are a couple different ways you can use the theorems for this.

You've observed that the 20 degree angle at A tells you that arc BC is 40 degrees, and then you can use the theorem pka talked about to find x = (40 + 76)/2 = 116/2 = 58 degrees, though you wrote that wrong.

It sounds like you haven't seen that theorem, though. That, and others, can be found here (among many other places): https://mathbitsnotebook.com/Geometry/Circles/CRAngles.html

Which of the theorems do you know? pka's is #4.

Now, here's the other way I had in mind: The inscribed angle theorem applied to arc AD tells us that angle B is 76/2 = 38 degrees. Then, looking at triangle ABX (taking point X to be the vertex of angle x), we have two interior angles, whose sum will be the other exterior angle. Have you learned about that? That makes x = 20 + 38 = 58 degrees. (This is one way to prove the other theorem.)

Again, we'll be happy to work with you as you study on your own. The more you tell us about what you've learned and show what you've tried, the more easily we can communicate with you and understand what help you need.
Click to expand...
Oh yes, I have learned that inscribed angles that intercept the same arc are congruent. I think I have done that at some point, but forgot to mention it. I also learned that opposite angles of a cyclic quadrilateral are supplementary. If I’m not mistaken, (which I probably am) aren’t there at least 8 theorems? I understood #4 as half of 40 first rather than half of the whole thing in parentheses. Thank you for suggesting the website, I will definitely take a look at it, and thank you for clarifying my doubt, I think I understand now.
 
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