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 ] ] ) )

Solve for `x`:

`x=` SOLUTION

var eq1 = A + "x + " + B + "^\\circ"; var 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( ANCHOR ); graph.pl.drawAngle( KNOWN_INDEX, eq1 ); graph.pl.drawAngle( UNKNOWN_INDEX, eq2, "#FFA500" );

We learned in Vertical angles 1 that vertical angles are equal. Watch this video to understand why.

Set the angle measures equal to one another.

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

Subtract `\color{PINK}{Cx}` from both sides.

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

`A - Cx + B = D`

B > 0 ? "Subtract" : "Add" `\color{PINK}{abs(B)}` B > 0 ? "from" : "to" both sides.

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

`A - Cx = D - B`

Divide both sides by `\color{PINK}{A - C}`.

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

Simplify.

`x = SOLUTION`

Subtract `\color{PINK}{Ax}` from both sides.

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

`B = C - Ax + D`

D > 0 ? "Subtract" : "Add" `\color{PINK}{abs(D)}` D > 0 ? "from" : "to" both sides.

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

`B - D = C - Ax`

Divide both sides by `\color{PINK}{C - A}`.

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

Simplify.

`SOLUTION = x`