document.write( "Question 1163536: Each side of Traingle ABC is produced. AB extends till D, AC extends till F and BC extends till E. If AB=AC, BD=BE and AF=DF, find angle ABC. \n" ); document.write( "
Algebra.Com's Answer #788095 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Each side of Traingle ABC is produced. AB extends till D, AC extends till F and BC extends till E. If AB=AC, BD=BE and AF=DF, find angle ABC.
\n" ); document.write( "
Borrowing Tutor @GREENESTAMPS' Diagram\r\n" );
document.write( ".\r\n" );
document.write( "AB = AC, so ∡ABC = ∡ACB\r\n" );
document.write( "BD = BE, so ∡BDE = ∡BED\r\n" );
document.write( "AF = DF, so ∡ADF = ∡FAD\r\n" );
document.write( "\r\n" );
document.write( "Let ∡BDE be x\r\n" );
document.write( "∡s BDE and ADF are the same\r\n" );
document.write( "Then ∡BDE, ∡BED, and ∡CAB are each, x, as well\r\n" );
document.write( "\r\n" );
document.write( "Since an exterior angle of a triangle is equal to the sum of its interior opposite angles, we can say that: ∡ABC = x + x, or 2x\r\n" );
document.write( "In addition, ∡ACB also = 2x (AB = AC)\r\n" );
document.write( "From ΔABC, its 3 angles are: x, 2x, and 2x. so we get: x + 2x + 2x = 180\r\n" );
document.write( "5x = 180\r\n" );
document.write( "\"matrix%281%2C5%2C+x%2C+%22=%22%2C+180%2F5%2C+%22=%22%2C+36o%29\"\r\n" );
document.write( "\r\n" );
document.write( "Therefore, ∡ABC = 2x = 2(36) = \"highlight_green%2872%5Eo%29\"
\n" ); document.write( "
\n" );