randRangeNonZero( -20, 20 ) randRange( 2, 9 ) randRangeNonZero( -200, 200 ) randRange( 2, 9 )
A * SOLUTION + B - C * SOLUTION (A*D-B*C) / (A-C) shuffle( randFromArray( [ [ 2, 4 ], [ 3, 1 ] ] ) )

Resuelve para x:

x= SOLUTION

var eq1=A+"x + "+B+"^\\circ",eq2=C+"x + "+D+"^\\circ";init({range:[[-1,5],[-1,1]]}),graph.pl=new ParallelLines(0,0,4,0,0),graph.pl.draw(),graph.pl.drawTransverse(KNOWN_INDEX%2===0?ANCHOR:180-ANCHOR),graph.pl.drawAngle(KNOWN_INDEX,eq1),graph.pl.drawAngle(UNKNOWN_INDEX,eq2,"#FFA500")

Aprendimos en Ángulos verticales 1 que los ángulos verticales son iguales Mira este video para entender por qué.

Establece las medidas de los ángulos iguales entre sí.

\color{BLUE}{Ax + B} = \color{ORANGE}{Cx + D}

Resta \color{PINK}{Cx} a ambos lados.

(Ax + B) \color{PINK}{- Cx} = (Cx + D) \color{PINK}{- Cx}

A - Cx + B = D

Resta \color{PINK}{abs(B)} a ambos lados.

Suma \color{PINK}{abs(B)} a ambos lados.

(A - Cx + B) \color{PINK}{+ -B} = D \color{PINK}{+ -B}

A - Cx = D - B

Divide ambos lados entre \color{PINK}{A - C}.

\dfrac{A - Cx}{\color{PINK}{A - C}} = \dfrac{D - B}{\color{PINK}{A - C}}

Simplifica.

x = SOLUTION

Resta \color{PINK}{Ax} a ambos lados.

(Ax + B) \color{PINK}{- Ax} = (Cx + D) \color{PINK}{- Ax}

B = C - Ax + D

Resta \color{PINK}{abs(D)} a ambos lados.

Suma \color{PINK}{abs(D)} a ambos lados.

B \color{PINK}{+ -D} = (C - Ax + D) \color{PINK}{+ -D}

B - D = C - Ax

Divide ambos lados entre \color{PINK}{C - A}.

\dfrac{B - D}{\color{PINK}{C - A}} = \dfrac{C - Ax}{\color{PINK}{C - A}}

Simplifica.

SOLUTION = x