## Thursday, December 23, 2010

### Problem 555: Parallel lines, Angles, Sum

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

Zoom
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.

2. http://img690.imageshack.us/img690/9956/problem555.png

Make polygon with 7 sides per attached pictures
Summation of internal angles= 5*180= 900
a+x+360-a+y+360-a+z+a=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