Thursday, December 23, 2010

Problem 555: Parallel lines, Angles, Sum

Geometry Problem
Click the figure below to see the complete problem 555.

 Problem 555: Parallel lines, Angles, Sum.
Level: High School, SAT Prep, College geometry


  1. Name the vertices of the chain in the clockwise direction, as A,B,C,D,E,F,G in that order.
    (starting from the initial point A of the ray L1 and ending with the initial point G of L2)
    Join CE. Through C draw a line parallel to L2 (or L1) cutting AB at H and DE at I;
    Through E draw a line parallel to the L1 cutting AB at J and FG at K.
    Consider the triangle CDI.
    Angle CDI= y (given).
    Using the property that in a triangle,
    the external angle at any vertex is the sum of internal angles at the other two vertices,
    it can be easily seen that angle DCI = x, angle CID = z.
    Follows x + y +z = 180 degrees.


    Make polygon with 7 sides per attached pictures
    Summation of internal angles= 5*180= 900
    So x+y+z=180

    Peter Tran

  3. draw at two upper vertexes of a paralleles to L1 or L2
    formed a triangle with angles x, y, z