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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the value of x? tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## What is the value of x? If a circle is circumscribed around a quadrilateral, as shown above, what is the value of x? A. 105 B. 110 C. 115 D. 120 E. 125 The OA is C. I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi AAPL, This question is built around one specific Geometry rule: when a quadrilateral is inscribed in a circle, opposite angles sum to 180 degrees. Thus, angle X =180 - 65 = 115 degrees. Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If a circle is circumscribed around a quadrilateral, as shown above, what is the value of x? A. 105 B. 110 C. 115 D. 120 E. 125 The OA is C. I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much. Hi AAPL, Let's take a look at your question. We know that the in a circle when two chords of a circle make an angle at the circumference of the circle, the arc subtended by that angle is always twice the angle. Therefore, in the circle given, $$2x\ =\ arclength\ \left(BAD\right) ... (i)$$ $$2\times65\ =\ arclength\ \left(BCD\right)$$ $$\ 130=\ arclength\ \left(BCD\right ... (ii))$$ Adding Eq(i) and (ii), $$\ 2x+130=\ arclength\ \left(BAD\right)+\ arclength\ \left(BCD\right)$$ $$\ 2x+130=\ 360$$ $$\ 2x=\ 360-130$$ $$\ 2x=\ 230$$ $$\ x=\ \frac{230}{2}=115$$ Therefore, Option C is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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