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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 ## Regular polygon X has r sides, and each vertex has... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Regular polygon X has r sides, and each vertex has... Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q? A. 2 B. 160 C. 176 D. 178 E. 179 The OA is C. Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q? A. 2 B. 160 C. 176 D. 178 E. 179 The OA is C. Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks. If we want to find the maximum possible angle measure for the interior angles of Q, we first need to find the max possible angle measure for X, as Q will have 1/4 as many sides as X. Equation for finding the sum of all interior angles of a polygon with 'n' sides: (n-2) * 180 Equation for finding the measure of each interior angle of a regular polygon with 'n' sides: (n-2)*180/n If the interior angles of X are integer values, then the greatest possible measure of each angle would be 179 degrees. (180 would be a straight line, and thus not a polygon.) To find the number of sides of a polygon with interior angles of 179, simply set the above equation to 179: (n-2)*180/n = 179 (n-2) *180 = 179n 180n - 360 = 179n -360 = -n n = 360 So X can have at most 360 sides. If Q has 1/4 the number of sides as X, then Q, at most, can have 360/4= 90 sides. If n = 90, each interior angle would be (90-2)*180/90 = 88*180/90 = 88*2 = 176. The answer is C _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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