Relations of Angles in a Triangle
Source:
June 13, 2009
Problem Statement
In a general triangle (as shown) lines and are drawn. Which of the following angle relations is true?
[asy]defaultpen(linewidth(.8pt));
unitsize(2cm);pair A = origin;
pair B = (1,0);
pair C = (2,0);
pair D = (3,0);
pair E = (1.25,1.75);draw(A--D--E--cycle);
draw(E--B);
draw(E--C);label("",A,SW);
label("",B,S);
label("",C,S);
label("",D,SE);
label("",E,N);
label("",E,3SW + 3S);
label("",E,7S + E);
label("",E,3SE + 4S + E);
label("",A,NE);
label("",B,NW);
label("",B,NE);
label("",C,NW);
label("",C,NE);
label("",D,NW+W);[/asy]
(A)\ x \plus{} z \equal{} a \plus{} b\qquad (B)\ y \plus{} z \equal{} a \plus{} b\qquad (C)\ m \plus{} x \equal{} w \plus{} n\qquad \\
(D)\ x \plus{} z \plus{} n \equal{} w \plus{} c \plus{} m\qquad (E)\ x \plus{} y \plus{} n \equal{} a \plus{} b \plus{} m