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clear this b4 leaving circles :) 550-600

by Night reader » Mon Nov 22, 2010 9:49 pm
If O is the center of a circle, find x?
A. 44
B. 35
C. 27
D. 30
E. 33

(figure is attached below)
Image
Last edited by Night reader on Mon Nov 22, 2010 11:38 pm, edited 1 time in total.
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by goyalsau » Mon Nov 22, 2010 10:09 pm
Night reader wrote:If O is the center of a circle, find x?
A. 44
B. 35
C. 27
D. 30
E. 33

(figure is attached below)
Image
I think answer should be
E - 33
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by Night reader » Mon Nov 22, 2010 10:24 pm
goyalsau wrote: I think answer should be
E - 33
you cleared the problem with a solution?
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by Night reader » Mon Nov 22, 2010 11:37 pm
goyalsau wrote:
Night reader wrote:If O is the center of a circle, find x?
A. 44
B. 35
C. 27
D. 30
E. 33

(figure is attached below)
Image
I think answer should be
E - 33
The question is open, we have no solution so far
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by beat_gmat_09 » Tue Nov 23, 2010 12:07 am
Agree with goyalsau, the answer is 33, below is my solution.


Image

refer above fig.


y+66+a=180 .......... (1)
x+(x+y)+a=180
a=180-2x-y
substitute a in (1)
y+66+180-2x-y=180
2x=66
x=33
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by Geva@EconomistGMAT » Tue Nov 23, 2010 12:28 am
An inscribed angle is half of the central angle that defines the same arc.

x is an inscribed angle lying on the same arc as a central angle. The central angle supplements 114 to 180 (straight line), so the central angle is 180-114=66. Thus, x must equal half of 66, or 33.
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by Night reader » Tue Nov 23, 2010 12:46 am
Geva@MasterGMAT wrote:An inscribed angle is half of the central angle that defines the same arc.

x is an inscribed angle lying on the same arc as a central angle. The central angle supplements 114 to 180 (straight line), so the central angle is 180-114=66. Thus, x must equal half of 66, or 33.
Thanks Geva!

Goyalsau and beat_gmat 09, this looks as we spend extra time here
https://www.analyzemath.com/Geometry/ins ... rcles.html
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by beat_gmat_09 » Tue Nov 23, 2010 12:47 am
Geva@MasterGMAT wrote:An inscribed angle is half of the central angle that defines the same arc.

x is an inscribed angle lying on the same arc as a central angle. The central angle supplements 114 to 180 (straight line), so the central angle is 180-114=66. Thus, x must equal half of 66, or 33.
Yeah, this is the best solution. I knew this one but it didn't struck me :o
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by Geva@EconomistGMAT » Tue Nov 23, 2010 1:09 am
beat_gmat_09 wrote:
Geva@MasterGMAT wrote:An inscribed angle is half of the central angle that defines the same arc.

x is an inscribed angle lying on the same arc as a central angle. The central angle supplements 114 to 180 (straight line), so the central angle is 180-114=66. Thus, x must equal half of 66, or 33.
Yeah, this is the best solution. I knew this one but it didn't struck me :o
There's a reason they placed the entire thing in a circle. In questions asking for angles in a circle, think inscribed/central angles first, then triangle properties 2nd.
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by beat_gmat_09 » Tue Nov 23, 2010 1:50 am
Geva@MasterGMAT wrote:
beat_gmat_09 wrote:
Geva@MasterGMAT wrote:An inscribed angle is half of the central angle that defines the same arc.

x is an inscribed angle lying on the same arc as a central angle. The central angle supplements 114 to 180 (straight line), so the central angle is 180-114=66. Thus, x must equal half of 66, or 33.
Yeah, this is the best solution. I knew this one but it didn't struck me :o
There's a reason they placed the entire thing in a circle. In questions asking for angles in a circle, think inscribed/central angles first, then triangle properties 2nd.
Thanks Geva !
Very useful.
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