What is X?

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hk: MBA Student; Posts: 532; Joined: Wed Jan 28, 2009 1:39 pmFollowed by: 9 members; Location: Barcelona; Thanked: 33 times; GMAT Score:640

by hk » Mon Apr 06, 2009 1:01 pm

Hello good people.

A quick question for you experts... <Please refer to the picture>

In the picture, if o is the center of the circle and angle ABO = Angle OBC = 30, then is it true that angle X is 120? If you could you please give an explanation on how its true.. Just wanted get my fundamentals clear!!!

Thanks a lot

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Source: Beat The GMAT — Problem Solving | Mon Apr 06, 2009 1:01 pm

pjasak: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Mar 20, 2009 7:51 am

by pjasak » Mon Apr 06, 2009 1:23 pm

This is my first posting here - hope it makes sense.

Sides of the triangles are both radii of the circle and are therefore equal making these isocoles triangles.
Therefore angle A = 30 degrees and the angle AOB = 180-30-30 = 120 so the opposing angle must be 60 dgerees.
These 2 opposing angles are the angle X so X must be 120 degrees.

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Mon Apr 06, 2009 4:08 pm

There is a geometry theorem which states that:

Angle subtended by the major arc at the center is twice the angle subtended by it at the circumference.

So, simply x = 2(30+30)

x= 2*60 = 120

Hope it is clear now

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