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

Subtract \color{PINK}{abs(B)} from both sides.

Add \color{PINK}{abs(B)} 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

Subtract \color{PINK}{abs(D)} from both sides.

Add \color{PINK}{abs(D)} 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