Stuck on this (Find the value of x from drawing of angles inside a circle)

[apple2357]

I have tried the various theorems and still getting nowhere, i am wondering if the question has enough in it?

 

[topsquark]

I have tried the various theorems and still getting nowhere, i am wondering if the question has enough in it?
View attachment 36455

ACB is equal to ADB.

Now you can find CAB.

AOB = 2 ACB.

Now you can find OAB.

Now you can find x.

-Dan

 

[Harry_the_cat]

I'm stuck too! How do you find CAB in the second step?

 

[pka]

I'm stuck too! How do you find CAB in the second step?

Notice that $\angle ADB~\&~\angle ACB$ are both inscribed angles intercepting the same arc,

 

[apple2357]

Notice that $\angle ADB~\&~\angle ACB$ are both inscribed angles intercepting the same arc,

I get that but still cant see how to find CAB? Apologies for being a dope!

 

[pka]

Can you see that $\Delta AOB$ is isosceles?
Can you see that $m(\angle AOB)=136^o$?
Can you see that $m(\angle OAB)=22^o$?
If so, surly you can finish?

$$

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[apple2357]

I use all that and i get to this point...

 

[Steven G]

I get the same angles as you get. Did you try to draw any additional lines or extend any lines? That might help! How about arc lengths?

Based on you work, how much is x+y equal to?

Does x=y!!!!

 

[lev888]

Seems like we can move points C and D around the circle while maintaining the 31 degree angles - this changes x.

 

[apple2357]

I get the same angles as you get. Did you try to draw any additional lines or extend any lines? That might help! How about arc lengths?

Based on you work, how much is x+y equal to?

Does x=y!!!!

I can't see how x could equal y unless you make an assumption

 

[topsquark]

I use all that and i get to this point...

View attachment 36456

Nope. You are absolutely correct. I played with this on Desmos and I came up with three different values for x, depending on where I put D and A.

-Dan

 

[apple2357]

Seems like we can move points C and D around the circle while maintaining the 31 degree angles - this changes x.

This suggests its is not a well formed question?

 

[apple2357]

Nope. You are absolutely correct. I played with this on Desmos and I came up with three different values for x, depending on where I put D and A.

-Dan

So you can still retain the 68 and 31 for different x?

 

[topsquark]

So you can still retain the 68 and 31 for different x?

Yes. Depending on where I put A after I set point D, I was able to construct x = 11.7 degrees, 12.4 degrees, and 2.5 degrees.

Try this. The angles don't measure perfectly, but it does okay and is simple to learn how to use.

-Dan

 

[Harry_the_cat]

I use all that and i get to this point...

View attachment 36456

Exactly what I have. x+y=37. But I can't see another relationship between x and y.

 

[Harry_the_cat]

Can you see that $\Delta AOB$ is isosceles?
Can you see that $m(\angle AOB)=136^o$?
Can you see that $m(\angle OAB)=22^o$?
If so, surly you can finish?

$$

$$

$$

$$

I am surly because I can't finish. What are you seeing that we aren't?

 

[Dr.Peterson]

Proof that the problem is not fully constrained: