Help needed for geometry/inscribed angle problem

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Sharnice

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Can someone tell me if I did this right? I understand that with inscribed angles, the big/outer angle is twice as big as the inner angle, however, this problem just states to solve for X. It didn't mention finding any angles or degrees ( I just wrote them in anyway because I like to show everything).
Thanks! problem 4.jpg
 
The triangle is isosceles. Therefore, measuring in degrees,

[MATH]\angle CDB = \angle DCB = 28 \implies[/MATH]
[MATH]\angle CBD = 180 - 2 * 28= 180 - 56 = 124.[/MATH] WHY?

[MATH]\angle CBD + \angle ABD = 180[/MATH] WHY?

[MATH]\therefore 3x + 1 + 124 = 180 \implies x = WHAT? [/MATH]
EDIT: Of course you can also go

[MATH]3x + 1 = 2 * 28 \implies 3x = 56 - 1 \implies x = WHAT?[/MATH]
You will get the same answer. What you labelled as x is wrong.
 
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JeffM said:
The triangle is isosceles. Therefore, measuring in degrees,

[MATH]\angle CDB = \angle DCB = 28 \implies[/MATH]
[MATH]\angle CBD = 180 - 2 * 28= 180 - 56 = 124.[/MATH] WHY?

[MATH]\angle CBD + \angle ABD = 180[/MATH] WHY?

[MATH]\therefore 3x + 1 + 124 = 180 \implies x = WHAT? [/MATH]
Click to expand...

I don't understand what you mean. Are you asking why I wrote certain things on the paper? I stated that I didn't think the 124 degrees and the 56 degrees were needed, which is why they weren't included in my equation. I was just making note of what those angles were.
 
Sharnice said:
Can someone tell me if I did this right? I understand that with inscribed angles, the big/outer angle is twice as big as the inner angle, however, this problem just states to solve for X. It didn't mention finding any angles or degrees ( I just wrote them in anyway because I like to show everything).
View attachment 14986
Click to expand...
You have the central angle theorem all wrong: The measure of a central angle equals the measure of the subtended arc.
Therefore \(\displaystyle 3x+1=56\)
 
Sharnice said:
I don't understand what you mean. Are you asking why I wrote certain things on the paper? I stated that I didn't think the 124 degrees and the 56 degrees were needed, which is why they weren't included in my equation. I was just making note of what those angles were.
Click to expand...
As pka explicitly noted and I implied in my edit, you have the central angle theorem wrong. Therefore, your answer is wrong. Measuring in degrees

[MATH]\angle CDB = 28.[/MATH]
You simply assumed that the measure of that angle was x. There was absolutely no basis for that assumption except some misunderstanding on your part of the central angle theorem. Moreover, you could have got the correct answer without reference to the central angle theorem had you proceeded as I indicated. Of course you would have got the same answer had you used the central angle theorem correctly.
 
In my first reply I was going with the given diagram. In it there is \(\displaystyle 3x+1\) and the question asks you to solve for that \(\displaystyle x\).
So you have another mistake in that you intruded a second \(\displaystyle x\). That is just not done.
In any case you should have seen at once that \(\displaystyle \Delta CDB\) is isosceles (the legs are radial segments) so \(\displaystyle m(\angle CDB)=28.\)
 
JeffM said:
As pka explicitly noted and I implied in my edit, you have the central angle theorem wrong. Therefore, your answer is wrong. Measuring in degrees

[MATH]\angle CDB = 28.[/MATH]
You simply assumed that the measure of that angle was x. There was absolutely no basis for that assumption except some misunderstanding on your part of the central angle theorem. Moreover, you could have got the correct answer without reference to the central angle theorem had you proceeded as I indicated. Of course you would have got the same answer had you used the central angle theorem correctly.
Click to expand...
@JeffM Well that's exactly why I asked for help. I was actually referencing the inscribed angle at 28 degrees, not the central angle theorem. So, forgive me for not instantly proceeding as you indicated; as I was still trying to process the steps myself. I'm sure you could have made your point without the sarcasm, being that everyone isn't so quickly inclined to understand math. Thanks for the help though.
 
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pka said:
In my first reply I was going with the given diagram. In it there is \(\displaystyle 3x+1\) and the question asks you to solve for that \(\displaystyle x\).
So you have another mistake in that you intruded a second \(\displaystyle x\). That is just not done.
In any case you should have seen at once that \(\displaystyle \Delta CDB\) is isosceles (the legs are radial segments) so \(\displaystyle m(\angle CDB)=28.\)
Click to expand...

Thank you. I see what you mean now and was able to find my mistakes. I appreciate your help
 
Well, there is a way to describe which angles you are talking about other than the "bigger, outer angle" or the "inner angle."

Had you said

"Given that the measure of angle DBA is twice that of angle DCA, then 3x + 1 = 2 * 28," it would have been clear that not involving the number 56 was not going to work and obvious that x < 37.7 degrees.
 
JeffM said:
Well, there is a way to describe which angles you are talking about other than the "bigger, outer angle" or the "inner angle."

Had you said

"Given that the measure of angle DBA is twice that of angle DCA, then 3x + 1 = 2 * 28," it would have been clear that not involving the number 56 was not going to work and obvious that x < 37.7 degrees.
Click to expand...
Again, I apologize for not stating it in a way that was suitable for you. I was asking for help, not rude criticism.
 
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