tailieunhanh - Master the Gre 2010 - Part 29

Peterson's Master the Gre 2010 - Part book includes 9 full-length practice tests , thorough reviews of every section on the exam, and expert tips and strategies from a test prep pro. GRE (Graduage Record Examination General Test) is a commercially-run standardized test and an admission requirement for many graduate schools in USA and other English-speaking countries. GRE can earn you between 200-800 points. | Chapter 11 Math Review Geometry 263 1. The figure above shows three intersecting lines. What is the value of x y 1 A 50 B 80 C 130 D 140 E 150 The correct answer is D . The angle vertical to the one indicated as being 40 must also measure 40 . That 40 angle together with the angles whose measures are x and y combine to form a straight 180 line. In other words 40 x y 180. Thus x y 140. A slightly tougher wheel-spoke question might focus on overlapping angles and require you to apply rule 1 about vertical angles to determine the amount of the overlap. Look at this wheel-spoke figure Degree measures of the individual central angles of a wheel-spoke figure total 360 which is the number of degrees in a circle. You ll explore this concept again later in the chapter. A GRE question about this figure might test your ability to recognize one of the following relationships 264 PART IV Quantitative Reasoning x y - z 180 x y exceeds 180 by the amount of the overlap which equals z the angle vertical to the overlapping angle. x y v w 360 The sum of the measures of all angles excluding z is 360 z is excluded because it is already accounted for by the overlap of x and y. y - w z w equals its vertical angle so y - w equals the portion of y vertical to angle z. Parallel Lines and Transversals GRE problems involving parallel lines also involve at least one transversal which is a line that intersects each of two or more lines. Look at this next figure in which 11 12 and I3 14 The upper-left cluster of angles numbered 1 2 3 and 4 matches each of the three other clusters. In other words All the odd-numbered angles are congruent equal in size to one another. All the even-numbered angles are congruent equal in size to one another. If you know the size of just one angle you can determine the size of all 16 angles. Chapter 11 Math Review Geometry 265 2. In the figure above lines P and Q are parallel to each other. If mZx 75 what is the measure of Zy A 75