randRange(6, 20) * randRangeNonZero(-1, 1) randRange(2, 8) randRangeNonZero(-200, 200) randRangeExclude(2, 9, [A, A - 1, A + 1])
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: [[-4, 4], [-1, 1]], scale: 60 }); 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, GREEN);

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.

`\blue{Ax + B^\circ} = \green{Cx + D^\circ}`

Subtract `\pink{Cx}` from both sides.

`(Ax + B^\circ) \pink{- Cx} = (Cx + D^\circ) \pink{- Cx}`

`A - Cx + B^\circ = D^\circ`

Subtract `\pink{abs(B)}^\circ` from both sides.

Add `\pink{abs(B)}^\circ` to both sides.

`(A - Cx + B^\circ) \pink{+ -B^\circ} = D \pink{+ -B^\circ}`

`A - Cx = D - B^\circ`

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

`\dfrac{A - Cx}{\pink{A - C}} = \dfrac{D - B^\circ}{\pink{A - C}}`

Simplify.

`x = SOLUTION^\circ`

Subtract `\pink{Ax}` from both sides.

`(Ax + B^\circ) \pink{- Ax} = (Cx + D^\circ) \pink{- Ax}`

`B^\circ = C - Ax + D^\circ`

Subtract `\pink{abs(D)^\circ}` from both sides.

Add `\pink{abs(D)^\circ}` to both sides.

`B^\circ \pink{+ -D^\circ} = (C - Ax + D^\circ) \pink{+ -D^\circ}`

`B - D^\circ = C - Ax`

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

`\dfrac{B - D^\circ}{\pink{C - A}} = \dfrac{C - Ax}{\pink{C - A}}`

Simplify.

`SOLUTION^\circ = x`