# Khan/khan-exercises

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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]);

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

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

Opposite angles of a parallelogram are equal.

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

Adjacent angles of a parallelogram are supplementary.

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

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

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

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]