Angle and Arc Problem: If <BEC = 71*, EF cong. EG, arc AB = 18*, arc AE = 3*arc CD,

[BigNate]

Angle and Arc Problem: If <BEC = 71*, EF cong. EG, arc AB = 18*, arc AE = 3*arc CD,

Hello Everyone,

I am struggling with question #18. The figure is shown in the attached image. The question is all about angle measurements and arc measurements. Here ios what I know so far...
Given: angle BEC = 71 degrees. This means arc BC is 172 degrees. However, it is after this point that I get stuck.

Can someone please point me on the right direction here?

Thanks!
Nate

 

[BigNate]

Sorry big boy...can't read your attachment.

Denis, I appreciate the effort and thank you for letting me know. Can you please provide more information? Is it the size of it that is giving you the issue or is there some other issue that is preventing you from reading it. Please let me know. Thank you.

 

[mmm4444bot]

if I click on it, the whole thing turns dark

I don't experience this issue; can you try a different web browser?

 

[mmm4444bot]

Given: angle BEC = 71 degrees. This means arc BC is 172 degrees.

Did you intend to type "142 degrees", for the arc measure of BC?

The measure of an inscribed angle is half the measure of its arc. :cool:

 

[mmm4444bot]

AB = 18 degrees means what?

That's the measure of arc AB (not to be confused with the length of arc AB).

EF ? EG : what does ? represent?

In geometry, that symbol means "is congruent to". In other words, line segments EF and EG have the same length.

 

[BigNate]

Thanks everyone. Just a little more help please and I think I will have it.

I'm confused as to what I need to figure out next. If EF is congruent to EG, is it fair to say arc CD is congruent to arc AB, which is 18 degrees? If so, that would be enough for me to solve the rest of the circle.

Thanks everyone for your help!

 

[BigNate]

Mark asked you if you meant arcBC=142, not 172.
How did you get 172?

Yes, that’s correct. I meant 142.

 

[mmm4444bot]

If EF is congruent to EG, is it fair to say arc CD is congruent to arc AB, which is 18 degrees?

No, I don't think we may jump to that conclusion.

Unfortunately, I have forgotten most of my classical circle-geometry. I have sent a message to MrsPi, to join the conversation. There must be a way to solve this question, without having to change the representative diagram.

I can say that triangle EFG is isosceles. This means that we can determine the measures of angles EFG and EGF. I don't know whether that helps or not.