randomQuadAngles.trapezoid() randRange( 0, 3 ) ANSWER_POS % 2 === 0 ? ( ANSWER_POS + 3 ) % 4 : ( ANSWER_POS + 1 ) % 4 function() { var a = ["", "", "", ""]; a[ANSWER_POS] = "x"; a[SHOWN_POS] = ANGLES[SHOWN_POS] + "^{\\circ}"; return a; }()
What is the value of the angle marked with `x`?
init({ range: [ [-1, 12 ], [ -8, -1 ] ] }) var q = new Quadrilateral([2, -7], ANGLES, randRange(0, 1) + 0.5, ""); q.boxOut( [ [ [ -0.5, -10 ], [ -0.5, 10 ] ] ], [ 0.1, 0 ] ); q.boxOut( [ [ [ 11.5, -10 ], [ 11.5, 10 ] ] ], [ -0.1, 0 ] ); q.draw(); q.labels = { "angles": ANG_LABELS, "sides": $.map($.map(q.sides, lineLength), function(x) { return localeToFixed(x * 4, 1); }) }; q.drawLabels(); ParallelLineMarkers((q.points[0][0] + q.points[3][0]) / 2, q.points[0][1]); ParallelLineMarkers((q.points[1][0] + q.points[2][0]) / 2, q.points[1][1]);
ANGLES[ ANSWER_POS ]`\Large{{}^\circ}`

This figure is a trapezoid.

The angles of a trapezoid side are supplementary.

`ANGLES[SHOWN_POS]^\circ + x = 180^\circ`

`x = 180^\circ - ANGLES[SHOWN_POS]^\circ`

`x = ANGLES[ANSWER_POS]^\circ`

randomQuadAngles.isoscelesTrapezoid()
randomQuadAngles.isoscelesTrapezoid() ANSWER_POS % 2 === 0 ? ( ANSWER_POS + 1 ) : ( ANSWER_POS - 1 )

This figure is an isosceles trapezoid.

The angles of bases of an isosceles trapezoid are equal.

Therefore, the angle `x` is also `ANGLES[SHOWN_POS]^\circ`

randomQuadAngles.parallelogram() ( ANSWER_POS + 2 ) % 4

This quadrilateral is a parallelogram.

Opposite angles of a parallelogram are equal.

Therefore, the angle `x` is also `ANGLES[SHOWN_POS]^\circ`

randomQuadAngles.parallelogram() ANSWER_POS % 2 === 0 ? ( ANSWER_POS + 1 ) : ( ANSWER_POS - 1 )

This quadrilateral is a parallelogram.

Adjacent angles of a parallelogram are supplementary.

`ANGLES[SHOWN_POS]^\circ + x = 180^\circ`

`x = 180^\circ - ANGLES[SHOWN_POS]^\circ`

`x = ANGLES[ANSWER_POS]^\circ`

randomQuadAngles.rhombus()
init({ range: [ [-1, 12 ], [ -8, -1 ] ] }) var q = new Quadrilateral( [ 2, -7 ], ANGLES, 1, "" ); q.boxOut( [ [ [ -0.5, -10 ], [ -0.5, 10 ] ] ], [ 0.1, 0 ] ); q.boxOut( [ [ [ 11.5, -10 ], [ 11.5, 10 ] ] ], [ -0.1, 0 ] ); q.draw(); q.labels = { "angles" : ANG_LABELS, "sides" : $.map( $.map( q.sides, lineLength ), function( x ){ return localeToFixed(x, 1); } ) }; q.drawLabels();

This quadrilateral is a rhombus, because it has all sides equal.

Opposite angles of a rhombus are equal.

Therefore, the angle `x` is also `ANGLES[SHOWN_POS]^\circ`

randomQuadAngles.rhombus() ANSWER_POS % 2 === 0 ? ( ANSWER_POS + 1 ) : ( ANSWER_POS - 1 )

This quadrilateral is a rhombus, because it has all sides equal.

Adjacent angles of a rhombus are supplementary.

`ANGLES[SHOWN_POS]^\circ + x = 180^\circ`

`x = 180^\circ - ANGLES[SHOWN_POS]`

`x = ANGLES[ANSWER_POS]^\circ`

randomQuadAngles.kite() randFromArray( [ 1, 3 ] ) ( ANSWER_POS + 2 ) % 4

This quadrilateral is a kite, because it has two pairs of adjacent sides equal.

Angles between the non-equal sides of a kite are equal.

Therefore, the angle `x` is also `ANGLES[SHOWN_POS]^\circ`