Gogeometry 696 - Model 1

[geo]

$ABC$ üçgeninin iç bölgesinde alınan $D$ noktası için $\angle ABD =x$, $\angle BAD=2x$, $\angle CAD = 5x$, $\angle ACD =3x$, $\angle BCD=4x$ ise $x=?$

size(9cm);

// x = 10  =>  A = 70, B = 40, C = 70  (BA = BC)
pair B = (0, 0);
pair C = (6, 0);
pair A = 6*dir(40);
// D: CBD = 30, BCD = 40
pair D = extension(B, B + dir(30), C, C + dir(140));

draw(A--B--C--cycle, black+1);
draw(A--D);
draw(B--D);
draw(C--D);

markangle("$x$", D, B, A, radius=1.1, black);
markangle("$2x$", B, A, D, radius=0.55, black);
markangle("$5x$", D, A, C, radius=0.85, black);
markangle("$3x$", A, C, D, radius=0.55, black);
markangle("$4x$", D, C, B, radius=0.9, black);

dot("$A$", A, N);
dot("$B$", B, W);
dot("$C$", C, E);
dot("$D$", D, S);

Kaynak: https://gogeometry.com/geometry/p696_triangle_angles_congruence_college.htm