Find angle DFE. Probably using inscribed angles, circle, chords, arcs.

DrGore

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I need to find the measurement of angle DFE. I'm guessing it has something to do with inscribed angles and arcs. Although I'm not really sure how I do have a fairly basic understanding of the two concepts.
 
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I need to find the measurement of angle DFE. I'm guessing it has something to do with inscribed angles and arcs. Although I'm not really sure how I do have a fairly basic understanding of the two concepts.

Ignore A and the lines passing through it. Have you seen a theorem dealing with the remaining figure, the arc measures and angle F?

If not, you can see that and others here.

You'll have to apply the theorem with a slight twist for your problem, but it's pretty direct.
 
Ignore A and the lines passing through it. Have you seen a theorem dealing with the remaining figure, the arc measures and angle F?

If not, you can see that and others here.

You'll have to apply the theorem with a slight twist for your problem, but it's pretty direct.

Firstly, thank you for that website! I had found that earlier and never bookmarked it and lost it in the sea of internet. Secondly, I seem to still be having some trouble. Through process of elimination the only one I think it can be is #4. But that requires me to know the lengths of the arcs at either end of the lines (in this case BC and DE. But I only know the inverse. I'm guessing there's some way to find that? But I'm unsure what that might be exactly.
 
Firstly, thank you for that website! I had found that earlier and never bookmarked it and lost it in the sea of internet. Secondly, I seem to still be having some trouble. Through process of elimination the only one I think it can be is #4. But that requires me to know the lengths of the arcs at either end of the lines (in this case BC and DE. But I only know the inverse. I'm guessing there's some way to find that? But I'm unsure what that might be exactly.

I mentioned a slight "twist". That was a bit of a pun. You have to sort of turn the picture to see it.

You're right that in order to directly use the theorem to find angle F, you would want to know arcs BC and DE. But what angle can you find using what is given? Can you use that to find F?

This is a useful idea in general: when you can't see how to get all the way to the answer, just think about what you can do with what you know, and what you might be able to use to get to the required result. Those pieces will help you see how to connect everything - like taking one step when you don't know the whole route.
 
what is meant by mCE=84, mBD=38?

The measure of an arc is the measure of the central angle; I would have specified that these are in degrees, but either the OP's course defines arc measures as always in degrees, or it was too hard to find the degree symbol.

So if the center of the circle is O, angle COE measures 84°, and angle BOD measures 38°.

Note that the picture is not at all to scale; the answer will not be the kind of number you expect. You might want to try drawing a more accurate sketch just to convince yourself it makes sense.
 
I mentioned a slight "twist". That was a bit of a pun. You have to sort of turn the picture to see it.

You're right that in order to directly use the theorem to find angle F, you would want to know arcs BC and DE. But what angle can you find using what is given? Can you use that to find F?

This is a useful idea in general: when you can't see how to get all the way to the answer, just think about what you can do with what you know, and what you might be able to use to get to the required result. Those pieces will help you see how to connect everything - like taking one step when you don't know the whole route.

That makes sense! I somehow made a calculation error and was really stuck but I guess I just typed some numbers wrong....several times...? That's really weird, but regardless thank you very much! I appreciate it a lot!
 
The measure of an arc is the measure of the central angle; I would have specified that these are in degrees, but either the OP's course defines arc measures as always in degrees, or it was too hard to find the degree symbol.

So if the center of the circle is O, angle COE measures 84°, and angle BOD measures 38°.

Note that the picture is not at all to scale; the answer will not be the kind of number you expect. You might want to try drawing a more accurate sketch just to convince yourself it makes sense.

I can't get it to work with coe 85o, bod 38o
I checked out the formulas for angles in circles.
Do you think ce is 84 units of arc length, and bd is 38? [and both measured clockwise, i.e. ce goes the long way around the circle].
then bod would be 38/r, where r is in radians, then the inscribed angle is 1/2 that, and so on.
 
I can't get it to work with coe 85o, bod 38o
I checked out the formulas for angles in circles.
Do you think ce is 84 units of arc length, and bd is 38? [and both measured clockwise, i.e. ce goes the long way around the circle].
then bod would be 38/r, where r is in radians, then the inscribed angle is 1/2 that, and so on.

No, I told you what it means, and that interpretation leads to the correct answer. There is no mention of any lengths at all; without the radius, arc lengths would be useless.

Did you look at the page I referred to previously listing the relevant theorems? The one you want is #4.
 
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