randRange(30, 150) randRange(0, 8) * Math.PI / 8
randRange(0, 7) (KNOWN_INDEX + 4) % 8 KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR MEASURE

Notice that the two angles are in the same position but at different intersections.

One way to describe the angles is to say that they are corresponding angles.

Corresponding angles are always equal.

shuffle(randFromArray([[0, 6], [1, 7]])) KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR MEASURE

Vertical angles are equal, so the pink angle measures `MEASURE` degrees.

graph.pl.drawVerticalAngle(KNOWN_INDEX, true, PINK);

The pink and green angles are corresponding angles, so they are also equal.

shuffle( randFromArray([[2, 4], [3, 5]])) KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR MEASURE

Vertical angles are equal, so the pink angle measures `MEASURE` degrees.

graph.pl.drawVerticalAngle( KNOWN_INDEX, true, PINK );

The pink and green angles are corresponding angles, so they are also equal.

shuffle(randFromArray([[1, 6], [0, 7]])) KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR 180 - MEASURE

The pink angles are adjacent to the blue angle and form a straight line, so they measure `180^\circ - MEASURE^\circ = 180 - MEASURE^\circ`.

graph.pl.drawAdjacentAngles( KNOWN_INDEX, true, PINK );

The pink angles are equal because they are opposite each other.

One of the pink angles corresponds with the green angle, and the other pink angle forms an alternate interior angle.

Angle `x` equals the pink angles and measures `SOLUTION^\circ`.

graph.pl.drawAngle(UNKNOWN_INDEX, true, GREEN);

Note that the blue and green angles are supplementary.

shuffle( randFromArray([[3, 4], [2, 5]])) KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR 180 - MEASURE

The pink angles are adjacent to the blue angle and form a straight line, so they measure `180^\circ - MEASURE^\circ = 180 - MEASURE^\circ`.

graph.pl.drawAdjacentAngles(KNOWN_INDEX, true, PINK);

The pink angles are equal because they are vertical angles.

One of the pink angles corresponds with the green angle, and the other pink angle forms an alternate exterior angle.

Angle `x` equals the pink angles and measures `SOLUTION^\circ`.

graph.pl.drawAngle(UNKNOWN_INDEX, true, GREEN);

Note that the blue and green angles are supplementary.

Below are two parallel lines with a third line intersecting them.

If we know that the blue angle is `MEASURE^\circ`, what is the measure of angle `x`?

init({ range: [[-4, 3], [-3, 3]], scale: 60 }); graph.pl = new ParallelLines(0, 0, 5.5, 2, ROTATION); graph.pl.draw(); graph.pl.drawMarkers(ANCHOR); graph.pl.drawTransverse(ANCHOR); graph.pl.drawAngle(KNOWN_INDEX, true); graph.pl.drawAngle(UNKNOWN_INDEX, "x", GREEN);

SOLUTION `^\circ`

Angle `x` is `SOLUTION^\circ`

graph.pl.drawAngle(UNKNOWN_INDEX, true, GREEN);