Geometry Problem

Click the figure below to see the complete problem 555.

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Level: High School, SAT Prep, College geometry

## Thursday, December 23, 2010

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

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## Thursday, December 23, 2010

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

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Online Geometry theorems, problems, solutions, and related topics.

Click the figure below to see the complete problem 555.

Zoom

Level: High School, SAT Prep, College geometry

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Name the vertices of the chain in the clockwise direction, as A,B,C,D,E,F,G in that order.

ReplyDelete(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.

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

ReplyDeleteMake 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

draw at two upper vertexes of a paralleles to L1 or L2

ReplyDeleteformed a triangle with angles x, y, z