I think that circle geometry questions can be some of the toughest, because a lot of times you have to be pretty creative. They also often involve triangles, even when they do not explicitly set it up for you like in this question.

This problem focuses heavily on the inscribed angle rule of circles. The inscribed angle rule is cousin to the central angle rule, and you treat inscribed angles the same as central angles but you double them. This means that the given 30 degree inscribed angle will etch out the equivalent of a 60 degree central angle between B and C. This means that the arcs from D to B on the left and from C to D on the right will each be the other 150 degrees of the circle (360 - 60 = 300, 300/2 = 150). Using the inscribed angle rule again, we see that x is an inscribed angle to the entire arc from B to C and C to D, or 60+150 = 210. Given that X is an inscribed angle and not a central angle, we use the rule in reverse and divide 210 by 2 in order to get X = 105 degrees, or answer choice E. Being able to reverse engineer rules (use rules backwards) is key to solving tricky gmat questions.

The inscribed angle rule is less well known than the central angle rule, so the gmat will use it to separate test takers. Make sure you are solid on all fundamental rules of geometry!

Veritas does an awesome job of highlighting these rules (which are necessary but definitely not sufficient to crushing the gmat), and then delving deeply into strategic use of the rules.

I hope this helps!

_________________

Brandon

Veritas Prep | GMAT Instructor

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