Given in circle b, measure of arc DCA = 316, find m<ACD

happiness

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Problem 44. I tried, truly lost on this one.
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Problem 44. I tried, truly lost on this one.

How did you get 316/2 = 92.94??

I would consider how the desired angle, ACD, is related to the known arc, DCA. Do you see how arc AD is related to each?

Here is a hint when you ask for help: rather than just show a calculation, it's a lot more useful to say in words what you are thinking. Then we can tell whether you just wrote the wrong number, or had an entirely wrong idea.

I presume you do know those circle theorems to which I gave you a reference in some thread; one of those is presumably what you have in mind here.
 
How did you get 316/2 = 92.94??

I would consider how the desired angle, ACD, is related to the known arc, DCA. Do you see how arc AD is related to each?

Here is a hint when you ask for help: rather than just show a calculation, it's a lot more useful to say in words what you are thinking. Then we can tell whether you just wrote the wrong number, or had an entirely wrong idea.

I presume you do know those circle theorems to which I gave you a reference in some thread; one of those is presumably what you have in mind here.
I did that because the arc looked like a half of the circle because AC is a diameter in the circle.

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The "that" that I am referring to is 316/2
I did that because the arc looked like a half of the circle because AC is a diameter in the circle.

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How did you get 316/2 = 92.94??

I would consider how the desired angle, ACD, is related to the known arc, DCA. Do you see how arc AD is related to each?

Here is a hint when you ask for help: rather than just show a calculation, it's a lot more useful to say in words what you are thinking. Then we can tell whether you just wrote the wrong number, or had an entirely wrong idea.

I presume you do know those circle theorems to which I gave you a reference in some thread; one of those is presumably what you have in mind here.
I don't know which to use, is it the 4th one?
http://jwilson.coe.uga.edu/emt725/ReviewCir/ReviewCir.htm

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No, there is no intersection of two chords. All you need is #1.

Don't miss the fact that B is the center of the circle.

But first, can you answer my questions? They were meant to help you along, so if you can answer even one part, it will give us more to talk about. The important thing is to think -- get moving, try something, and you will have things to think about and learn from. Don't wait until you know just what to do.
 
I did that because the arc looked like a half of the circle because AC is a diameter in the circle.

Arc AC is half a circle; but that is not what they are asking about.

Do you understand that arc DCA is the long arc that starts at D, passes through C, and ends at A?
 
Yes I do, I feel like I am getting no where. Is the answer C since 1/3(100) = 66.66 repeating?
Arc AC is half a circle; but that is not what they are asking about.

Do you understand that arc DCA is the long arc that starts at D, passes through C, and ends at A?

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I am completely bewildered and these type of problems are foreign to me I don't understand not one thing about them. I don't get #1.
No, there is no intersection of two chords. All you need is #1.

Don't miss the fact that B is the center of the circle.

But first, can you answer my questions? They were meant to help you along, so if you can answer even one part, it will give us more to talk about. The important thing is to think -- get moving, try something, and you will have things to think about and learn from. Don't wait until you know just what to do.

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Yes I do, I feel like I am getting no where. Is the answer C since 1/3(100) = 66.66 repeating?

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You really need to stop using a calculator. Otherwise you will keep saying things like 316/2 = 92.94. There are many things I can say about that. First of all 316 is even so when divided by 2 there will be no decimals. 2ndly, 316 is more than 300. It is even much more than 200. If you divide 200 by 2 you get more than 92.94, so how are you dividing 316 by 2 and only getting 92.94. I myself make arithmetic mistakes all the time but I catch almost all of them because I think and realize my result does not make sense. If you use a machine to do your calculation you will make many more mistakes then doing the problem by hand or in your head. Why? Because you type in numbers and might miss one digit or type it in wrong and get the wrong answer. The other reason not to use electronics is that it makes math boring and more difficult.

Angle ACD cuts off arc AD. If you know the measure of arc AD you divide it by 2 and then you measure of angle ACD. The problem you face is that you do not know the measure of arc AD. Knowing that the there are 360 degrees in a circle and using the measure of an arc that you are given can you find the measure of arc AD? If this is still troubling you, then highlight the arc that you want to find the measure of and using a different color highlight the arc that you know the measure of. The light bulb in your head will then light up. Please return and tell us how you made out.
 
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MISTER Happiness, you're told that arcDCA = 316 degrees:
that means that if you start from D and go CLOCKWISE,
you will go through C then continue to A; you've now
travelled 316 degrees.
So if you continue from A to starting point D,
how many degrees will you travel?
44. 360-316

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44. 360-316

Good. Now, which theorem relates this arc (which is also the central angle) to the angle you are interested in (called an inscribed angle)?



Assuming that you were taught (some of) those theorems, the key to solving a problem like this is to look for relationships that might be useful (based on various theorems or other facts you have learned), and then try to put those together to make a path from what you know to what you have to find. The idea of finding the minor arc from the major arc was one step, and this theorem will be another.

Often in problem solving I will start by looking for anything I can fill in immediately based on what I am given (in this case, marking various arcs or angles), and also mark the thing I need to find. Then I stare at it, looking for any further relationships that might take me in the right direction.
 
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