Anubisboy

Are you certain this statement is correct? In the above expression, odd power of [math]i[/math] should be not real.

Following the link located at the lower left hand corner of the diagram, I found the problem at this site as well. ([url=http://www.gogeometry.com/problem/problem013.htm][/url]http://www.gogeometry.com/problem/problem013.htm). However, the description of the problem doesn't completely match the diagram for the problem. There must be an error in either the diagram or description.

Bignose, I may be making a mistake, but after solving the equations you provided, I didn't get obtain a result for [math]x[/math]. Equation one implies [math] BDC=180-8x[/math], and equation three implies [math]ABD=180-12x[/math]. Substituting the result from equation 3 into equation 2 gives [math]4x+ADB+180-12x=180 \Longrightarrow ADB=8x[/math]. Substituting the result for [math]ABD[/math] plus the result obtained for [math]BDC[/math] into equation four yields [math] 180-8x+8x=180 \Longrightarrow 180=180[/math], which, while true, is not very revealing. I think one must make use of the fact that [math]AB=CD[/math]. How this is done is not readily apparent to me. Anubisboy